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The value of the integralint0^(3alpha) c...

The value of the integral`int_0^(3alpha) cosec(x-alpha) cosec(x-2alpha)dx` is

A

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

B

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

C

`2 cosec alpha log (sec alpha)`

D

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

Text Solution

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The correct Answer is:
D
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  2. int0^(2pi) e^(x/2) sin (x/2+pi/4) dx =

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  3. The value of the integralint0^(3alpha) cosec(x-alpha) cosec(x-2alpha)d...

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  4. lim(n rarr oo) { n/(n^(2)+1^(2)) + n/(n^(2)+2^(2))+......+ n/(n^(2)+n^...

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  5. The value of the integral int0^(pi/4) (sin theta + cos theta)/(9+16 si...

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  6. int(0)^(1//2) |sin pi x| dx is equal to :

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  7. The value of int(-pi/2)^(pi/2) |x cos ((pix)/2)| dx is

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  8. For any integer n, the integral : int0^(pi) e^(cos^2) cos^(3) (2n + 1)...

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  9. If g(x) = int0^x cos^4 t dt, then g(x + pi) equals:

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  10. If I(n) = int0^(pi/4) tan^(n) theta d theta, then I(8)+I(6) equals

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  11. The value of int0^(pi/2) (1)/(1+tan^(3)x) dx is

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  12. Let f : R to R and g : R to R be continuous functions. Then the value ...

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  13. If f(a + b - x) = fx, then inta^b x f(x) dx is equal to :

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  14. int0^(pi/2) (dx)/(1+cotx) =

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  15. If f and g are continuous [0,a) satisfying f(x) = f(a-x) and g(x)+ g(a...

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  16. int0^(3) |x^(3)+x^(2)+3x| dx is equal to

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  17. int0^(10) |x(x-1)(x-2)| dx is equal to

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  18. If I = int0^(pi/4) log (1+ tan x) dx, then I =

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  19. lim(n rarr oo) {1/n+1/(n+1)+1/(n+2)+…..+1/(3n)} =

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  20. If I = int(-pi)^(pi) (e^(sinx))/(e^(sinx)-e^(-sinx)) dx then I =

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