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If g(x)=int(sinx)^("sin"(2x))sin^(-1)(t)...

If `g(x)=int_(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n :`
(a) `g^(prime)(pi/2)=-2pi` (b) `g^(prime)(-pi/2)=-2pi` (c) `g^(prime)(-pi/2)=2pi` (d) `g^(prime)(pi/2)=2pi`

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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