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If int x^2e^(-2x)= e^(-2x)(ax^2+bx+c)+d ...

If `int x^2e^(-2x)= e^(-2x)(ax^2+bx+c)+d` then

A

`a= -(1)/(2)`

B

`b =(1)/(2)`

C

`c= -(1)/(4)`

D

`d in R`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`intx^(2)e^(-2x)dx=e^(-2x)(ax^(2)+bx+c)+d`
Differentiating both sides, we get
`x^(2)e^(-2x)=e^(-2x)(2ax+b)+(ax^(2)+bx+c)(-2e^(-2x))`
`=e^(-2x)(-2ax^(2)+2(a-b)x+b-2c)`
`or a=(-1)/(2),2(a-b)=0,b-2c=0`
` or b=(-1)/(2),c=(-1)/(4)`
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