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

`int_(0)^(pi//4) log (1+tan x) dx =?`

A

`(1)/(2) pi log 8`

B

`(1)/(8) pi log 2`

C

`(1)/(4) pi log 2`

D

None of these

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The correct Answer is:
B
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ML KHANNA-DEFINITE INTEGRAL-ProblemSet (2) (Multiple Choice Questions)
  1. int(0)^(pi//2) (a sin x +b cos x)/(sin x+cos x) dx=

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

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

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

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

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

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

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

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

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

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

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

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

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  14. int(0)^(pi) e^(cos^(2)x) cos^(3) (2n+1) x dx, (n in I)=

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  15. int(0)^(pi) (x sin x)/(1+ cos^(2) x)dx=

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  16. Prove that :int(0)^(pi//2) (x sin x cos x)/(sin^(4) x+ cos^(4)x)dx =(p...

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  17. int(pi)^(5pi//4) (sin 2x)/(cos^(4) x +sin^(4)x) dx=

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  18. Prove that :int(0)^(pi) (x)/(a^(2) cos^(2) x+b^(2) sin^(2) x)dx =(pi^(...

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  19. int(0)^(pi/2)logsinx=-(pi/2)log2 int(0)^(pi) x log sin x dx=

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  20. If I(1)= int(0)^(pi) x f {sin^(3) x +cos^(2)x} dx and I(2)= pi int(0)^...

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