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Integrals

Question
CBSEENMA12036201
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integral subscript 0 superscript straight pi space xf space left parenthesis sin space straight x space right parenthesis space dx is equal to
  • straight pi integral subscript 0 superscript straight pi space straight f left parenthesis cos space straight x right parenthesis space dx
  • straight pi integral subscript 0 superscript straight pi space straight f left parenthesis sin space straight x right parenthesis space dx
  • straight pi over 2 integral subscript 0 superscript straight pi space straight f left parenthesis cos space straight x right parenthesis space dx
  • straight pi integral subscript 0 superscript straight pi divided by 2 end superscript space straight f left parenthesis cos space straight x right parenthesis space dx

Solution

D.

straight pi integral subscript 0 superscript straight pi divided by 2 end superscript space straight f left parenthesis cos space straight x right parenthesis space dx straight I space equals space integral subscript 0 superscript straight pi xf space left parenthesis sin space straight x right parenthesis space dx equals space integral subscript 0 superscript straight pi left parenthesis straight pi minus straight x right parenthesis space straight f left parenthesis sin space straight x right parenthesis space dx space equals integral subscript 0 superscript straight pi straight f left parenthesis sin space straight x right parenthesis space dx space minus straight l 2 straight l space equals space integral subscript 0 superscript straight pi straight f left parenthesis sin space straight x right parenthesis space dx straight l space equals space straight pi over 2 integral subscript 0 superscript straight pi space straight f left parenthesis sin space straight x right parenthesis space dx space equals straight pi space integral subscript 0 superscript straight pi divided by 2 end superscript space straight f space left parenthesis sin space straight x right parenthesis space dx equals straight pi integral subscript 0 superscript straight pi divided by 2 end superscript space straight f left parenthesis cos space straight x right parenthesis space dx

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