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Prove that: int(0)^(pi//2) (sinx)/(sinx ...

Prove that: `int_(0)^(pi//2) (sinx)/(sinx +cos x) dx =(pi)/(4)`

A

`(pi)/(2)`

B

`pi`

C

`(pi)/(4)`

D

none

Text Solution

Verified by Experts

The correct Answer is:
C
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ML KHANNA-DEFINITE INTEGRAL-ProblemSet (2) (Multiple Choice Questions)
  1. Prove that: int(0)^(pi//2) (sinx)/(sinx +cos x) dx =(pi)/(4)

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  2. int(0)^(a) (dx)/(x+ sqrt""(a^(2) -x^(2)))=

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  3. The value of the integral int(0)^(pi//2) (sqrt""(cot x))/(sqrt""(cot x...

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  4. int(0)^(pi//2) (sqrt""(sin^(3).x) dx)/(sqrt""(sin^(3) x) + sqrt""(cos^...

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  5. The value of int(0)^(pi//2) (dx)/(1+tan^(3) x) is

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  6. int(0)^(pi) (dx)/(1 + tan^(4)x)=

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  7. The value of the integral int(0)^(pi//2) (phi (x))/(phi (x) + phi ((p...

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  8. int(0)^(pi//2) (a sin x +b cos x)/(sin x+cos x) dx=

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  9. int(0)^(oo) (xdx)/((1+x) (1+x^(2)))=

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  10. int(0)^(pi//4) log (1+tan x) dx =?

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  11. int(0)^(1) (log (1+x))/(1+ x^(2)) dx is equal to

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  12. int(0)^(pi) sin^(n) x.cos^(2m+1) xdx is equal to

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  13. int(0)^(pi//2) ((cos x-sin x))/((1+sin x cos x)) dx

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  14. int(0)^(pi//2) (cos 2x)/((sin x +cos x)^(2)) dx=

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  15. int(1//2)^(2) (1)/(x) cosec^(101) (x-(1)/(x))dx=

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  16. Given that int(0)^(pi//2) sin^(4) x cos^(2) x dx= (pi)/(32), then int(...

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

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  18. int(0)^(pi//2) (dx)/(sqrt(tan x)- sqrt(cot x))=

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  19. The value of int(0)^(pi) (2^(sin x)cos x)/(s^([sin x])).dx when [.] de...

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  20. The value of the integral int(0)^(pi//2) sin 2x log tan x dx equals

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