Archive
15th of March 2017
Mathematics
Q:

Evaluate integral subscript negative 2 end subscript superscript 2 space space space fraction numerator x squared over denominator 1 plus space 5 to the power of x end fraction space space d x

Ahuja8087 Ahuja - CBSE - Class XII Science

Wednesday, March 15, 2017 at 16:46:PM

A:

begin mathsize 16px style straight I equals integral subscript negative 2 end subscript superscript 2 fraction numerator straight x squared over denominator 1 plus 5 to the power of straight x end fraction dx space space space space space...... open parentheses straight i close parentheses
straight I equals integral subscript negative 2 end subscript superscript 2 fraction numerator open parentheses negative 2 plus 2 minus straight x close parentheses squared over denominator 1 plus 5 to the power of open parentheses negative 2 plus 2 minus straight x close parentheses end exponent end fraction dx
straight I equals integral subscript negative 2 end subscript superscript 2 fraction numerator straight x squared over denominator 1 plus 5 to the power of open parentheses negative straight x close parentheses end exponent end fraction dx
straight I equals integral subscript negative 2 end subscript superscript 2 fraction numerator straight x squared over denominator 1 plus begin display style 1 over 5 to the power of straight x end style end fraction dx
straight I equals integral subscript negative 2 end subscript superscript 2 fraction numerator 5 to the power of straight x straight x squared over denominator 1 plus begin display style 5 end style begin display style blank to the power of straight x end style end fraction dx space space space space....... open parentheses ii close parentheses
Adding space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma
2 straight I equals integral subscript negative 2 end subscript superscript 2 fraction numerator 5 to the power of straight x straight x squared plus straight x squared over denominator 1 plus begin display style 5 end style begin display style blank to the power of straight x end style end fraction dx
2 straight I equals integral subscript negative 2 end subscript superscript 2 fraction numerator open parentheses 5 to the power of straight x plus 1 close parentheses straight x squared over denominator 1 plus begin display style 5 end style begin display style blank to the power of straight x end style end fraction dx
2 straight I equals integral subscript negative 2 end subscript superscript 2 straight x squared dx
2 straight I equals 2 integral subscript 0 superscript 2 straight x squared dx
straight I equals open vertical bar straight x cubed over 3 close vertical bar squared subscript 0
straight I equals 2 cubed over 3
straight I equals 8 over 3 end style

Wednesday, March 15, 2017 at 17:47:PM