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Evaluate the following integrals using p...

Evaluate the following integrals using properties of integration `:`
`int_(0)^(sin^(2)x) sin^(-1) sqrt(t) dt + int_(0)^(cos^(2)x)sqrt(t) dt`

A

`g'((pi)/2)=-2pi`

B

`g'(-(pi)/2)=2pi`

C

`g'((pi)/2)=2pi`

D

`g'(-(pi)/2)=-2pi`

Text Solution

Verified by Experts

`g(x)=int_(sinx)^(sin(2x))sin^(-1)(t)dt`
`impliesg'(x)=2(cos2x)sin^(-1)(sin2x)-(cosx)sin^(-1)(sinx)`
`impliesg'((pi)/2)=2(-1)(0)-cos((pi)/2)(1)=0`
Also `g'(-(pi)/2)=0`
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