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int(-1)^(0)(dx)/(x^(2)+2x+2) is equal to...

`int_(-1)^(0)(dx)/(x^(2)+2x+2)` is equal to

A

0

B

`pi//4`

C

`pi//2`

D

`-pi//4`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int_(-1)^(0)(dx)/(x^(2)+2x+2)`
`=int_(-1)^(0)(dx)/((x+1)^(2)+1)`
`=[tan^(-1)((x+1)/(1))]_(-1)^(0)`
`=tan^(-1)(1)-tan^(-1)(0)`
`=(pi)/(4)`
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