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If l(1)=int sin^(-1)x dx and l(2) =int s...

If `l_(1)=int sin^(-1)x dx` and `l_(2) =int sin^(-1)sqrt(1-x^(2))dx`, then

A

`l_(1)=l_(2)`

B

`l_(2)=(pi)/(2)l_(1)`

C

`l_(1)+l_(2)=(pi)/(2)x`

D

`l_(1)+l_(2)=(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `l_(1)=int sin^(-1)xdx`
and `l_(2)=int sin^(-1)sqrt(1-x^(2))dx rArr l_(2)=int cos^(-1)xdx`
Now, `l_(1)+l_(2)=int(sin^(-1)x+cos^(-1)x)dx=int(pi)/(2)dx=(pi)/(2)x`
`therefore" "l_(1)+l_(2)=(pi)/(2)x`
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