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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)`

Text Solution

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The correct Answer is:
B
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MODERN PUBLICATION-DEFINITE INTEGRALS-RECENT COMPETITIVE QUESTIONS
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  3. If [x] denote the greatest integer function , then , int(0)^(pi//6) (1...

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  7. int0^(pi//4) (sin x + cos x)/(3 + sin 2x ) dx =

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  8. int0^1 (x^4 + 2x^2 + 1)d(x^2 + 1) =

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  9. If I(1)= int(0)^(pi//2) x sin x dx and I(2)=int(0)^(pi//2) x cos x dx,...

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

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  11. int0^pi (cos^4 x)/(cos^4 x + sin^4 x) dx =

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  12. If f(x) = f(pi + e - x) and inte^(pi) f(x) dx = 2/(e + pi), then inte^...

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  13. The value of the integral int(-pi//4)^(pi//4)log(sec theta-tan theta...

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  14. The interval I such that int0^1 (dx)/(sqrt(1 + x^4)) in I is given by ...

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  15. int0^(pi//2) log(tan x)dx =

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  16. The value of int(-2)^(2)(ax^(3)+bx+c) dx depends on the

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  17. int(0)^(pi//4)log ((sin x +cos x )/(cosx))dx is equal to

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  18. int(-pi//4)^(pi//4)(dx)/(1+cos 2x) is equal to

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  19. int(-1)^(1) (x^(27) cos x + e^x) dx =

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  20. The value of the integral int0^pi (x sin^(2n) x)/(sin^(2n) x + cos^(2n...

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

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