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I(m, n)= int(0)^(1) x^(m) (ln x)^(n) dx=...

`I_(m, n)= int_(0)^(1) x^(m) (ln x)^(n) dx=`

A

0

B

`(n)/(m+1)`

C

`-(n)/(m+1) I_(m-1, n)`

D

`- (n)/(m+1) I_(m, n-1)`

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
  1. If I(n) = int(0)^(pi//4) Tan^(n) x dx then I(2)+I(4), I(3)+I(5), I(4)+...

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  2. If I(n)=int(0)^(pi//4) tan^(n) x dx then {:(" " Lt),(n rarr oo):}n(I(n...

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  3. I(m, n)= int(0)^(1) x^(m) (ln x)^(n) dx=

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  4. Lt(xto0)(x^(2))/(int(0)^(x)Tan^(-1)tdt)

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  5. {:(" " Lt),(x rarr 0):} (int(0)^(x^(2))sec^(2) t dt)/(x sin x) =

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  6. Let f:RtoR be a differentiable function having f(2)=6,f'(2)=(1)/(48).T...

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  7. Let P(x) be a function defined on R such that P(x) = P'(1--x), AA x in...

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  8. If I(1) = int(1)^(2)(dx)/(sqrt(1+x^(2))) and I(2)= int(1)^(2) (dx)/(x)...

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  9. If I(1)= int(0)^(3pi) f( sin^(2) x)dx and I(2)= int(0)^(pi) f(sin^(2)x...

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  10. I= int(0)^(1)e^(x^(2))dx rArr

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  11. If I(1) = int(0)^(1) 2^(x^(2))dx, I(2) = int(0)^(1) 2^(x^(3))dx, I(3) ...

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  12. If [x] denotes the greatest integer less than or equal to x then int(1...

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  13. int(0)^(oo)[(2)/(e^(x))]dx=

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  14. Let I = int(0)^(1) (sin x)/(sqrt(x)) dx and J= int(0)^(1) (cos x)/(sqr...

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  15. Which of the following is true Statement-I : int(0)^(2pi) sqrt((1-cos2...

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  16. Which of the following are false : Statement-I : (int(0)^(pi//2) (sq...

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  17. Which of the following are true: I : int(0)^(4) sqrt(x^(2)-4x +4)dx=...

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  18. Arrange the following according to their values in ascending order A...

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  19. If 2 int(0)^(1) tan^(-1) x dx = int(0)^(1) cot^(-1) (1- x+x^(2))dx, th...

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  20. Arrange the following according to their values in ascending order A...

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