CBSE Class 12-science Answered

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 is $fraction numerator pi left parenthesis pi minus 2 alpha right parenthesis over denominator 2 cos alpha end fraction$

Asked by ahuja8087 | 15 Mar, 2017, 05:42: PM

Expert Answer

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

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

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

For the detailed solution post your query in Ask the Expert. Or you could also, click a picture of the solution you have done.

And we shall help you proceed with it. No need to type the solution here. Just upload an image of what you have done. It would be convenient for you. Thank you.

Answered by | 15 Mar, 2017, 06:08: PM