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The value of the integral int(0)^(3alp...

The value of the integral
`int_(0)^(3alpha) cosec (x-alpha)cosec(x-2alpha)dx` is

A

`2"sec" alpha log((1)/(2)"cosec" alpha)`

B

`2 "sec" alpha log((1)/(2)"sec "alpha)`

C

`2 "cosec" alpha log ("sec" alpha)`

D

`2 " cosec " alpha log((1)/(2)sec alpha)`

Text Solution

Verified by Experts

The correct Answer is:
D
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. The value of the integral int(0)^(2pi)(sin2 theta)/(a-b cos theta)d ...

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  2. The value of the integral int(0)^(1) x(1-x)^(n)dx, is

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

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  4. The value of the integral int(0)^(pi) (sin k x)/(sin x)dx (k is an eve...

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  5. The value of the integral int(0)^(1)(1)/(x^(2)+2x cos alpha+1)dxis equ...

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

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

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  8. The value of the integral int(0)^(pi//4) sin^(-4)x dx, is

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

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

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  11. The value of integral int(-pi)^(pi) (cos ax-sin b x)^(2)dx, where (a a...

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  12. The value of the definite integral int(0)^(1)(1+e^(-x^(2))) dx is

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

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

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  15. 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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  16. int(0)^(1//2) |sin pi s|dx is equal to

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  17. The function F(x)=int(0)^(x) log((1-x)/(1+x))dx, is

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

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

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  20. If F(x)and g(x) are two integralable functions defined on [a,b], the...

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