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For any integer n, the integral : int0^(...

For any integer n, the integral : `int_0^(pi) e^(cos^2) cos^(3) (2n + 1)x dx` has the value :

A

`pi`

B

1

C

0

D

none of these

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. int(0)^(1//2) |sin pi x| dx is equal to :

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. lim(x rarr oo) (int(0)^(2x) xe^(2)dx)/(e^(4x^(2))) equals :

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  17. The value of int(-2)^(2) { p log ((1+x)/(1-x))+ q log ((1-x)/(1+x))^(...

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  18. inta^(b) |x|/x dx, (Where 0 lt a lt b) =

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  19. The area of the region bounded by the curve y^(2)=8x and the line y=2x...

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  20. The area bounded by y = 4x-x^(2) and x-axis is

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