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The value of the integral int(-pi)^(pi)(...

The value of the integral `int_(-pi)^(pi)(cos^(2)x)/(1+a^(x))"dx"`, where `a gt 0`, is -

A

`pi`

B

`a pi`

C

`(pi)/(2)`

D

`2pi`

Text Solution

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The correct Answer is:
C
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ML KHANNA-DEFINITE INTEGRAL-Problem set (4) (Multiple Choice Questions)
  1. The value of int(0)^(2pi) cos^(99) x dx is

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  2. int(a)^(b) (f(x))/(f(x) +f(a+b-x))dx=

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  3. int(1)^(5) (sqrt""x)/(sqrt""(6-x) + sqrt""x) dx=

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  4. int(3)^(6) (sqrt""x)/(sqrt""(9-x) + sqrt""x) dx=

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  5. If f(a+b-x)= f(x), then int(a)^(b) x f(x) dx is equal to

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  6. If overset(b)underset(a)int (x^(n))/(x^(4)+(16-x)^(n))dx=6, then

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  7. If f(3-x)= f(x), then int(1)^(2) xf(x) dx is equal to

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  8. For any t in R and f be a continuous function Let I(1)= int(sin^(2)t...

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  9. If f(x) is an integrable function in ((pi)/(6), (pi)/(3)) and I(1)= in...

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  10. Let f be a positive function. Let I(1) int(1-k)^(k) x.f {x(1-x)} dx, I...

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  11. If f(x)= (e^(x))/(1+e^(x)), I(1)= int(f(-a))^(f(a)) xg {x(1-x)}dx and ...

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  12. The value of int(1//n)^((a n-1)//n) (sqrtx)/(sqrt(a-x) + sqrtx)dx is e...

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  13. If [x] stands for the greatest integer function, the value of int(4)^(...

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  14. int(pi//4)^(3pi//4) (dx)/(1+ cos x) is equal to

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  15. int(-pi//2)^(pi//2) (cos x dx)/(1+ e^(x))=

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  16. int(0)^(pi) (dx)/(1+2^(tan x))=

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  17. int(-pi//2)^(pi//2) (pi^(sin x))/(1+ pi^(sin x))dx=

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  18. The value of int(-pi//2)^(pi//2) (dx)/(e^(sin x) +1) is equal to

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  19. int(0)^(pi) (dx)/(1+ 4^(cos x))=

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  20. The value of the integral int(-pi)^(pi)(cos^(2)x)/(1+a^(x))"dx", where...

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