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Evaluate int(0)^(1)log(sin((pix)/(2)))dx...

Evaluate `int_(0)^(1)log(sin((pix)/(2)))dx`

A

log 2

B

`-log 2`

C

`(pi)/(2)log 2`

D

`-(pi)/(2) log 2`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. The value of int0^1 (x^(3))/(1+x^(8))dx is

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  2. The value of int(0)^(3) xsqrt(1+x)dx, is

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  3. Evaluate int(0)^(1)log(sin((pix)/(2)))dx

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  4. Evaluate int(0)^(pi) xlog sinx dx

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  5. If I(1)=int(0)^(oo) (dx)/(1+x^(4))dx and I(2)=underset(0)overset(oo)i...

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  6. If f(x)={{:(x,xlt1),(x-1,xge1):}, then underset(0)overset(2)intx^(2)f(...

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  7. The value of the integral overset(1)underset(0)int (1)/((1+x^(2))^(3//...

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  8. Prove that: int0^(2a)f(x)dx=int0^(2a)f(2a-x)dxdot

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  9. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

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  10. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

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  11. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

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  12. The value of the integral int 0^oo 1/(1+x^4)dx is

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  13. The value of alpha in [0,2pi] which does not satify the equation int(p...

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  14. lim(x to 0)(int(0)^(x^(2))sinsqrt(t) dt)/(x^(3)) is equl to

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  15. If [int0^1(dt)/(t^2+2tcosalpha+1)]x^2-[int- 3^3(t^2sin2t)/(t^2+1)dt]x-...

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  16. The number of value of alpha in the interval [-pi,0] satisfying sin...

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  17. The value of int(0)^(pi//2) (sin^(3)x cos x)/(sin^(4)x+ cos^(4)x )dx i...

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  18. The value of int0^pi1/(5+3cosx)dx is a. pi//2 b. pi//4 c. 0 d. pi...

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  19. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin((n-1))/...

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  20. underset(nrarr0)" lim" underset(r=1)overset(n)sum((r^(3))/(r^(4)+n^(4)...

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