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Home / Doubts and Solutions/JEE/Mathematics

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Asked by araima2001 25th December 2017, 1:55 PM
Answered by Expert
Answer:
begin mathsize 16px style straight I equals integral subscript negative straight pi end subscript superscript straight pi straight f left parenthesis 2 plus straight x right parenthesis sinxdx..... left parenthesis 1 right parenthesis Using space integral subscript negative straight a end subscript superscript straight a straight f left parenthesis straight x right parenthesis dx equals integral subscript negative straight a end subscript superscript straight a straight f left parenthesis negative straight x right parenthesis dx straight I equals integral subscript negative straight pi end subscript superscript straight pi straight f left parenthesis 2 minus straight x right parenthesis sin left parenthesis negative straight x right parenthesis dx straight I equals integral subscript negative straight pi end subscript superscript straight pi minus straight f left parenthesis 2 minus straight x right parenthesis sinxdx....... left parenthesis 2 right parenthesis Adding space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis 2 straight I equals integral subscript negative straight pi end subscript superscript straight pi open square brackets straight f left parenthesis 2 plus straight x right parenthesis minus straight f left parenthesis 2 minus straight x right parenthesis close square brackets sinxdx straight I equals 1 half integral subscript negative straight pi end subscript superscript straight pi open square brackets straight f left parenthesis 2 plus straight x right parenthesis minus straight f left parenthesis 2 minus straight x right parenthesis close square brackets sinxdx As space function space is space even. straight I equals 2 cross times 1 half integral subscript 0 superscript straight pi open square brackets straight f left parenthesis 2 plus straight x right parenthesis minus straight f left parenthesis 2 minus straight x right parenthesis close square brackets sinxdx equals integral subscript 0 superscript straight pi open square brackets straight f left parenthesis 2 plus straight x right parenthesis minus straight f left parenthesis 2 minus straight x right parenthesis close square brackets sinxdx Solve space it space further. space end style
Answered by Expert 26th December 2017, 12:06 PM
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Tags: evaluating-definite-integrals definite-integral problems-on-definite-integrals
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