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If f(y) = e^(y), g(y) = y , y > 0 and ...

If `f(y) = e^(y), g(y) = y , y > 0`
and `F(t) = int_0^t f(t - y) g(y) dy`, then

A

`F(t) = e^(t) - (1+t)`

B

`F(t) = t. e^(t)`

C

`F(t) = t. e^(-1)`

D

`F(t) = 1- e^(t)(1+t)`

Text Solution

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The correct Answer is:
A
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  3. If f(y) = e^(y), g(y) = y , y > 0 and F(t) = int0^t f(t - y) g(y) dy...

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  4. Let f(x) be a function satisfying f'(x) = f(x) with f(0) = 1 and g(x) ...

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  7. The value of int(-2)^3 |1 - x^2| dx is:

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  8. If int0^pi x f (sin x)dx = A int0^(pi//2) f (sin x) dx, then A is :

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  9. Let F : R to R be a differentiable function having : f(2) = 6, f'(2) =...

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  10. int0^(pi) x f (sin x) dx is equal to :

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  11. int(-3pi//2)^(-pi//2) [(x +pi)^3 + cos^2 (x + 3x)]dx is equal to :

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  12. If f(x) ={(e^(cosx)sinx; |x| le 2),(2 ; othe...

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  13. The value of integral int(e^(-1))^(e^2) |(loge x)/(x)| dx is :

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  14. Let g(x) = int0^(x) f(t) dt, where 1/2 le f(t) < 1, t in [0,1] and 0 <...

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  15. The value of int(-pi)^(pi) (cos^2 x)/(1 + a^x) dx, a > 0, is :

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  16. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

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  17. Let f(x) = int1^x sqrt(2 - t^2) dt. Then the real roots of the equatio...

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  18. The integral int(-1//2)^(1//2) ([x] + ln ((1 + x)/(1 - x)))dx equals :

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  19. If I(m,n) = int0^1 t^m (1 + t)^n dt , m, n in R, then I(m, n) is :

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  20. The value of the integral int0^1 sqrt((1 - x)/(1 + x))dx is :

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