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The value of the integral I=int(0)^(1)x(...

The value of the integral `I=int_(0)^(1)x(1-x)^(n)dx` is equal to

A

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

B

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

C

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

D

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

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Exercise
  1. The value of integral underset(a)overset(b)int(|x|)/(x)dx, a lt b is :

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  2. The value of the integral int(0)^(2pi)(sin2 theta)/(a-b cos theta)d ...

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  3. The value of the integral I=int(0)^(1)x(1-x)^(n)dx is equal to

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  4. The value of the integral int(0)^(3alpha) cosec (x-alpha)cosec(x-2al...

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  5. The value of the integral int(0)^(pi)(sin 2k x)/(sin x)dx, where k in...

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  6. The value of the integral int0^1(dx)/(x^2+2xcosalpha+1) is equal to si...

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  7. The greater value of F(x)=int(1)^(x) |t|dt on the interval [-1//2,1//2...

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  8. The value of the integral int(0)^(pi//2) |sin x-cos x|dx, is

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  9. The value of the integral int(-pi//4)^(pi//4) sin^(-4)x dx, is

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  10. The value of the integral I=int(1)^(oo) (x^(2)-2)/(x^(3)sqrt(x^(2)-1))...

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  11. int(0)^(1) |sin 2pi x|dx id equal to

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  12. Evaluate: int(-pi)^pi(cosa x+s in b x)^2dx

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  13. The value of the definite integral int0^1(1+e^-x^2)dx (b) 2 1+e^...

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  14. If I=int(-pi)^(pi) (sin^(2))/(1+a^(x))dx, a gt 0, then I equals

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  15. If n is an odd natural number, then int(-pi//6)^(pi//6) (pi+4x^(n))/...

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  16. If I(1)=int(0)^(x) e^("zx ")e^(-z^(2))dz and I(2)=int(0)^(x) e^(-z^(2)...

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  17. int(0)^(1//2) |sin pi x|dx is equal to

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  18. If f(x)=int(0)^(x) log ((1-t)/(1+t)) dt, then discuss whether even or ...

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  19. int(1//3)^(3) (1)/(x)sin ((1)/(x)-x)dx is equal to

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  20. If F(x)=int(x^(2))^(x^(3)) log t dt (x gt 0), then F'(x) equals

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