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15th of March 2017
Mathematics
Q:

Evaluate : integral subscript 0 superscript pi fraction numerator x space space space space d x over denominator 1 plus space sin alpha space sin x end fraction Answer isfraction numerator pi left parenthesis pi minus 2 alpha right parenthesis over denominator 2 cos alpha end fraction

Ahuja8087 Ahuja - CBSE - Class XII Science

Wednesday, March 15, 2017 at 17:42:PM

A:

begin mathsize 16px style Use space integral subscript 0 superscript straight a space straight f left parenthesis straight x right parenthesis space dx equals space space integral subscript 0 superscript straight a space straight f left parenthesis straight a space minus space straight x right parenthesis space dx space to space evaluate.
Also comma space remember space that space sin left parenthesis straight pi minus straight x right parenthesis equals sinx
Further space on comma space use space the space property comma space
If space straight f left parenthesis 2 straight a minus straight x right parenthesis equals straight f left parenthesis straight x right parenthesis comma space then integral subscript 0 superscript 2 straight a end superscript space straight f left parenthesis straight x right parenthesis space dx equals 2 space space integral subscript 0 superscript straight a space straight f left parenthesis straight x right parenthesis space dx
end style

Dear student, this is again a very lengthy solution. We have given you a hint on how you should go about it.

begin mathsize 16px style Also comma space remember space that space somewhere space while space you space evaluate space you space will space have space to space use space the space formula comma
sinx equals fraction numerator 2 tan begin display style straight x over 2 end style over denominator 1 plus tan squared open parentheses straight x over 2 close parentheses end fraction end style

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Wednesday, March 15, 2017 at 18:08:PM