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The value of the integral I = int0^1 x ...

The value of the integral `I = int_0^1 x (1 - x)^(n) dx` is :

A

1/(n+2)

B

1/(n+1)-1/(n+2)

C

1/(n+1)+1/(n+2)

D

1/(n+1)

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The correct Answer is:
B
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  6. Let f(x) be a function satisfying f'(x) = f(x) with f(0) = 1 and g(x) ...

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

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

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

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

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

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

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

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

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

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

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