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If I=int(0)^(1//2) (sin^(2)n x)/(sin^(2)...

If `I=int_(0)^(1//2) (sin^(2)n x)/(sin^(2)x)dx`then which one of the following is not true ?

A

`I_(n)=(npi)/(2)`

B

`I_(n)=2overset(pi//2)underset(0)int (sin x cos x 2n x)/(sin x)dx`

C

`I_(1),I_(2),I_(3),……I_(n)`… is a A.P.

D

sin`(I_(15))`=0

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The correct Answer is:
D
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. If I=int(3)^(4) (1)/(3sqrt(logx))dxthen

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  2. If I=int(0)^(1//2) (1)/(sqrt(1-x^(2n)))dxthen which one of the follow...

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  3. If I=int(0)^(1//2) (sin^(2)n x)/(sin^(2)x)dxthen which one of the foll...

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  4. For any integer n, the integral int0^pie^(cosx)cos^3(2n+1)xdx has the ...

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  5. The value of the integral int(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal...

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  6. If int(0)^(oo) (log(1+x^(2)))/(1+x^(2))dx=kint(0)^(oo) (log(1+x))/(1+x...

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  7. If int(log2)^(x) (1)/(sqrt(e^(x)-1))dx=(pi)/(6)then x is equal to

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  8. The value of the integral overset(pi)underset(0)int log(1+cos x)dx is

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  9. The integral int(0)^(pi) (1)/(a^(2)-2 a cos x+1)dx (a lt 1) is

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  10. The integral int(0)^(pi//2) f(sin 2 x)sin x dx is equal to

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  11. int(0)^(pi) k(pix-x^(2))^(100)sin2x" dx" is equal to

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  12. The value of the integral int(2)^(4) (sqrt(x^(2)-4))/(x^(4))dx is

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  13. The value of the integral int(0)^(pi)(1)/(a^(2)-2a cos x+1)dx (a gt1),...

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  14. If f(x) and g(x) are continuous functions satisfying (x)=f(a-x) and g(...

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  15. int0^(pi//2) x(sqrt(tan x)+sqrt(cot x))dx equals

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  16. The value of the integral int(1//3)^(1)((x-x^(3))^(1//3))/(x^(4))dx ...

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  17. The value of the integral int(0)^(100pi) sqrt(1-cos2x)" d"xis

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  18. The value of the integral int(-1//2)^(1//2) {((x+1)/(x-1))^(2)+((x-...

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  19. The value of the integral int(1//e)^(e) |logx|dx, is

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  20. The value of int(0)^(pi//2) (sin 8x log cot x)/(cos 2x)dx, is

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