Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

Please help to solve this problem
 
Asked by rajuharan | 26 Jan, 2017, 07:47: PM
answered-by-expert Expert Answer
begin mathsize 16px style Let space straight I equals integral subscript negative 2 end subscript superscript 2 space space fraction numerator straight x squared over denominator 1 plus 5 to the power of straight x end fraction dx space space space...... left parenthesis straight i right parenthesis
We space know space that comma space integral subscript straight a superscript straight b space space straight f left parenthesis straight x right parenthesis space dx equals space integral subscript straight a superscript straight b space space straight f left parenthesis straight a plus straight b minus straight x right parenthesis space dx
So comma space straight I space equals integral subscript negative 2 end subscript superscript 2 space space fraction numerator left parenthesis 2 plus left parenthesis negative 2 right parenthesis minus straight x right parenthesis squared over denominator 1 plus 5 to the power of 2 plus left parenthesis negative 2 right parenthesis minus straight x end exponent end fraction dx
rightwards double arrow straight I equals integral subscript negative 2 end subscript superscript 2 space space fraction numerator left parenthesis 2 plus left parenthesis negative 2 right parenthesis minus straight x right parenthesis squared over denominator 1 plus 5 to the power of 2 plus left parenthesis negative 2 right parenthesis minus straight x end exponent end fraction dx
rightwards double arrow straight I equals integral subscript negative 2 end subscript superscript 2 space space fraction numerator left parenthesis negative straight x right parenthesis squared over denominator 1 plus 5 to the power of negative straight x end exponent end fraction dx
rightwards double arrow straight I equals integral subscript negative 2 end subscript superscript 2 space space fraction numerator straight x squared over denominator 1 plus 5 to the power of negative straight x end exponent end fraction dx space space space...... left parenthesis ii right parenthesis
Adding space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get
2 straight I equals integral subscript negative 2 end subscript superscript 2 space space fraction numerator straight x squared over denominator 1 plus 5 to the power of straight x end fraction dx plus integral subscript negative 2 end subscript superscript 2 space space fraction numerator straight x squared over denominator 1 plus 5 to the power of negative straight x end exponent end fraction dx
rightwards double arrow 2 straight I equals integral subscript negative 2 end subscript superscript 2 space space fraction numerator straight x squared over denominator 1 plus 5 to the power of straight x end fraction dx plus integral subscript negative 2 end subscript superscript 2 space space fraction numerator 5 to the power of straight x straight x squared over denominator 1 plus 5 to the power of straight x end fraction dx
rightwards double arrow 2 straight I equals integral subscript negative 2 end subscript superscript 2 space space fraction numerator straight x squared plus 5 to the power of straight x straight x squared over denominator 1 plus 5 to the power of straight x end fraction dx space
rightwards double arrow 2 straight I equals integral subscript negative 2 end subscript superscript 2 space space fraction numerator straight x squared left parenthesis 1 plus 5 to the power of straight x right parenthesis over denominator 1 plus 5 to the power of straight x end fraction dx space
rightwards double arrow 2 straight I equals integral subscript negative 2 end subscript superscript 2 space space fraction numerator straight x squared left parenthesis 1 plus 5 to the power of straight x right parenthesis over denominator 1 plus 5 to the power of straight x end fraction dx space
rightwards double arrow 2 straight I equals integral subscript negative 2 end subscript superscript 2 space space straight x squared dx
rightwards double arrow 2 straight I equals 2 integral subscript 0 superscript 2 space space straight x squared dx space.... left parenthesis Since space straight x squared space is space even right parenthesis
rightwards double arrow straight I equals integral subscript 0 superscript 2 space straight x squared dx
rightwards double arrow straight I equals right enclose straight x cubed over 3 end enclose squared subscript 0
rightwards double arrow straight I equals 2 cubed over 3 equals 8 over 3 end style
Answered by Rebecca Fernandes | 27 Jan, 2017, 04:36: PM
CBSE 12-science - Maths
Asked by jprathamesh023 | 23 Mar, 2024, 04:01: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by atulmishra514 | 26 Jan, 2024, 10:15: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by ritiksingh84835808 | 19 Jan, 2023, 06:26: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by anshuman.anshuman090 | 24 Jan, 2020, 06:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by shobhit | 22 Feb, 2019, 11:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×