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int (0) ^((pi//2)^(1//3)) x ^(5). sin x ...

`int _(0) ^((pi//2)^(1//3)) x ^(5). sin x ^(3) dx` equal to

A

1

B

`1//2`

C

2

D

`1//3`

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The correct Answer is:
D
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. If f(0) = 1, f(2) = 3, f'(2) = 5 and f'(0) is finite, then int0^1 xf''...

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  2. If I (1) = int (e) ^(e ^(2)) (dx )/( ln x ) and I (2) = int (1) ^(2) (...

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  3. int (0) ^((pi//2)^(1//3)) x ^(5). sin x ^(3) dx equal to

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  4. If A=int(0)^(pi)cosx/(x+2)^2.dx, then int(0)^(pi/2)sin(2x)/(x+1).dx i...

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  5. If f(x)={0 ,where x=n/(n+1), n =1, 2, 3.... and 1 , else w...

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  6. If f(pi)=2 and int(0)^(pi)(f(x)+f''(x))sin x dx=5, then f(0) is equal ...

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  7. int(0) ^(pi//2) ((sin x +cos x )^(2))/sqrt(1+ sin 2x)dx =

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  8. int (0) ^(2) (x - log (2) a ) dx =2 log (2) ((2)/(a)), if

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  9. If overset(x)underset(log2)int (1)/(sqrt(e^(x)-1))dx=(pi)/(6)then x is...

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  10. If f(x) is a continuous function and attains only rational values in [...

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  11. If f(y)=e^(y), g(y)=y, y gt 0 and F(t)=int(0)^(t) f(t-y)g(y)dy, then ...

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  12. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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  13. int(0) ^(pi//2) ((sin x +cos x )^(2))/sqrt(1+ sin 2x)dx =

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  14. int (0) ^(pi//4) sin (x- [x])d (x-[x]) is equal to

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  15. For 0 lt x lt pi/2, int (1//sqrt2) ^(1//2) cot x s (cos x ) equal to

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  16. The value of int (pi//4) ^(pi//3) cosec x d (sin x ) for 0 lt x lt pi...

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  17. Find the value of : int0^(10)e^(2x-[2x])d(x-[x])w h e r e[dot] denote...

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  18. int (log pi - log 2 ) ^(log pi) (e ^(x))/(1- cos ((2)/(3)e ^(x)))dx i...

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  19. If underset(0)overset(oo)int e^(-x^(2))dx=sqrt((pi)/(2))"then"underset...

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  20. Let A = underset(0)overset(1)int(e^(t))/(1+t) dt, then underset(a-1)ov...

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