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Ifint(pi/3)^xsqrt((3-sin^2t))dt+int0^yco...

`Ifint_(pi/3)^xsqrt((3-sin^2t))dt+int_0^ycostdt=0,t h e ne v a l u a t e(dy)/(dx)`

Text Solution

Verified by Experts

The correct Answer is:
`(-sqrt(3)-sin^(2)x)/(cosy)`
We have `int_(pi//3)^(x)(sqrt(3-sin^(2)t))dt+int_(0)^(y)costdt=0`
Differentiating w.r.t `x`
`d/(dx) int_(pi//3)^(x)sqrt((3-sin^(2)t))dt+d/(dx)int_(0)^(y)cos dt =0`
or `sqrt((3-sin^(2)x))+cosy(dy)/(dx)=0`
or `(dy)/(dx)=(sqrt((3-sin^(2)x)))/(cosy)`
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