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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
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Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
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Function: initiateCache

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Function: require_once

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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
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Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
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Function: initiateCache

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Function: require_once

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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 17
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Line: 18
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

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Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 799
Function: get

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 605
Function: getComment

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

자유게시판
수학을 주제로 떠들어 보세요!
[잡담] 질문이 있어요
Scubed 2021.02.28 21:41 조회 500

로그 적분 함수에서 적분구간을 0으로 할때도 있고 2로 할때도 있다던데 그렇게 해도 결과적으로 값은 같게 나오나요? 계산기 돌리니깐 0으로 하면 자꾸 적분 안된다고 하던데ㅣ.........

 

https://namu.wiki/w/%EB%A1%9C%EA%B7%B8%20%EC%A0%81%EB%B6%84%20%ED%95%A8%EC%88%98

여기 개요에 마지막 줄

  •  
    △π Lv.9 2021.02.28 23:56

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    Filename: libraries/Common.php

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    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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    Function: is_dir

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    Filename: libraries/Common.php

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    Backtrace:

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    Line: 202
    Function: mkdir

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
    Line: 236
    Function: getLatexImg

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    Function: require_once

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    Filename: libraries/Common.php

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    Backtrace:

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    Line: 212
    Function: file_exists

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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    Function: getLatexImg

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
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    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
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    Function: require_once

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    Filename: libraries/Common.php

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    Backtrace:

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
    Line: 213
    Function: file_put_contents

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
    Line: 236
    Function: getLatexImg

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
    Line: 90
    Function: parseLatexImg

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
    Line: 343
    Function: view

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
    Line: 558
    Function: view

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
    Line: 315
    Function: require_once

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    Line Number: 213

    Backtrace:

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
    Line: 213
    Function: file_put_contents

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
    Line: 236
    Function: getLatexImg

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
    Line: 90
    Function: parseLatexImg

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
    Line: 343
    Function: view

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
    Line: 558
    Function: view

    File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
    Line: 315
    Function: require_once

    \mu 이하로 떨어지면 함숫값이 음수면서 1 제외하면 모두 정의되니까 0부터 적분하면 2부터 적분한 값 보다 더 작아지지 않을까요?

    로그 적분함수는 책에서만 잠깐 보고 넘겨서 잘 모르겠네요ㅠㅠ

    댓글 작성하기 좋아요0 댓글수2
    •  
      Scubed Lv.7 2021.03.01 00:25

      그러니까요......어째서 적분 구간이 바뀌어도 값이 같을 수가 있는지.....

      좋아요0
    •  
      △π Lv.9 2021.03.01 00:56

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      Filename: libraries/Common.php

      Line Number: 201

      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 201
      Function: is_dir

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 236
      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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      Function: require_once

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      Filename: libraries/Common.php

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      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 202
      Function: mkdir

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 236
      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
      Line: 315
      Function: require_once

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      Filename: libraries/Common.php

      Line Number: 212

      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 212
      Function: file_exists

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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      Function: require_once

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      Filename: libraries/Common.php

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      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 213
      Function: file_put_contents

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 236
      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
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      Function: require_once

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      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 213
      Function: file_put_contents

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 236
      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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      Function: require_once

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      Filename: libraries/Common.php

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      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 201
      Function: is_dir

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 236
      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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      Line: 315
      Function: require_once

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      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 202
      Function: mkdir

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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      Function: require_once

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      Filename: libraries/Common.php

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      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 212
      Function: file_exists

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 213
      Function: file_put_contents

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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      Function: getLatexImg

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      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
      Line: 558
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
      Line: 315
      Function: require_once

      A PHP Error was encountered

      Severity: Warning

      Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

      Filename: libraries/Common.php

      Line Number: 201

      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 201
      Function: is_dir

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 236
      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
      Line: 558
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
      Line: 315
      Function: require_once

      A PHP Error was encountered

      Severity: Warning

      Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

      Filename: libraries/Common.php

      Line Number: 202

      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 202
      Function: mkdir

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 236
      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
      Line: 558
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
      Line: 315
      Function: require_once

      A PHP Error was encountered

      Severity: Warning

      Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/da296876f0f111ff8b1f641051e4c201.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

      Filename: libraries/Common.php

      Line Number: 212

      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 212
      Function: file_exists

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 236
      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
      Line: 558
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
      Line: 315
      Function: require_once

      A PHP Error was encountered

      Severity: Warning

      Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/da296876f0f111ff8b1f641051e4c201.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

      Filename: libraries/Common.php

      Line Number: 213

      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 213
      Function: file_put_contents

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 236
      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
      Line: 558
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
      Line: 315
      Function: require_once

      A PHP Error was encountered

      Severity: Warning

      Message: file_put_contents(/DATA/upload/polymath/latex/da296876f0f111ff8b1f641051e4c201.gif): Failed to open stream: Operation not permitted

      Filename: libraries/Common.php

      Line Number: 213

      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 213
      Function: file_put_contents

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
      Line: 236
      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
      Line: 558
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
      Line: 315
      Function: require_once

      @Scubed

      아니면 \mu가 1.5 정도이고 2가 아님을 봐서 

      [0,\mu]의 적분값이 [\mu,2]에 근사한다고 생각할 수도 있을 것 같아요 

      맞는지는 잘 모르겠습니다ㅠㅠ

      좋아요0

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Article_model::$best_cnt is deprecated

Filename: ver3/Article_model.php

Line Number: 18

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Article_model.php
Line: 18
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 322
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 392
Function: getFloatingMyInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 559
Function: get_footer

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Article_model::$popular_cnt is deprecated

Filename: ver3/Article_model.php

Line Number: 19

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Article_model.php
Line: 19
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 322
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 392
Function: getFloatingMyInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 559
Function: get_footer

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

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