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Let g(x) be differentiable on R and int(...

Let `g(x)` be differentiable on `R` and `int_(sint)^1x^2g(x)dx=(1-sint),` where `t in (0,pi/2)dot` Then the value of `g(1/(sqrt(2)))` is____

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The correct Answer is:
2
We have `int_(sint)^(1) x^(2)g(x)dx=(1sint)`…………1
Differentiating both the sides of 1 with respect to `t` we get
`0-(sin^(2)t)g(sint)(cost)=-cost`
or `g(sint)=1/(sin^(2)t)`…………….2
Putting `t=(pi)/4` in (2) we get `g(1/(sqrt(2)))=2`.
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  6. Let f(x)=int(0)^(x)(dt)/(sqrt(1+t^(3))) and g(x) be the inverse of f(x...

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  7. Let g(x) be differentiable on R and int(sint)^1x^2g(x)dx=(1-sint), wh...

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