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If f(x) = int ((x^(2) + sin ^(2)x))/(1+x...

If `f(x) = int ((x^(2) + sin ^(2)x))/(1+x^(2))sec^(2)` x dx and f(0) = 0, then f(1) is :

A

`1-(pi)/(4)`

B

`(pi)/(4)`

C

`tan 1+(pi)/(4)`

D

`tan1+1`

Text Solution

Verified by Experts

The correct Answer is:
c
We have , `f(x)=int {((x^(2)+1)+(1-sin^(2)x))/(1+x^(2))}sec^(2)x dx`
`rArrf(x)=int(sec^(2)x+(1)/(1+x^(2)))dx`
`rArrf(x)=tanx+tan^(-1)x+C`
`thereforef(0)=0rArrC=0`
Hence , `f(x) tanx+tan^(-1)x`
`rArrf(1)=tan1+(pi)/(4)`
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