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If f(x)=int(5x^8+7x^6)/((x^2+1+2x^7))dx,...

If `f(x)=int(5x^8+7x^6)/((x^2+1+2x^7))dx,(xge0)andf(0)=0`, then the value of f(1) is

A

`-1/4`

B

`-1/2`

C

`1/4`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
C
If `f(x)=int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx=int((5)/(x^(6))+(7)/(x^(8)))/((2+(1)/(x^(7))+(1)/(x^(5)))^(2))dx`
`"Put "2+(1)/(x^(7))+(1)/(x^(5))=t`
`((-7)/(x^(8))-(5)/(x^(6)))dx=dt," "-int(dt)/(t^(2))=(1)/(t)`
`f(x)=(1)/(2+(1)/(x^(7))+(1)/(x^(5)))+C: f(0)=0=C rArr f(1)=(1)/(4)`
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