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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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CENGAGE-DEFINITE INTEGRATION -Exercise (Numerical)
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  5. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

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  8. If int0^oox^(2n+1)dote^(-xdx)=360 , then the value of n is

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  15. The value of the definite integral int(2-1)^(sqrt(2)+1)(x^4+x^2+2)/((x...

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  16. Consider a real valued continuous function f such that f(x)=sinx + int...

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  19. The value of int(1)^(3)(sqrt(1+(x-1)^(3))+(x^(2)-1)^(1/3)+1)dx is .

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