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int(pi//6)^(pi//3) (dx)/(1 + sqrt(tan x)...

`int_(pi//6)^(pi//3) (dx)/(1 + sqrt(tan x)) =`

A

`pi/12`

B

`pi/2`

C

`pi/6`

D

`pi/4`

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The correct Answer is:
A
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. int0^(pi/2) (cos theta)/(sqrt(4-sin^(2) theta) )d theta =

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  2. The value of the integral int0^(2a) (f(x))/(f(x) + f(2a - x)) is :

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  3. int(pi//6)^(pi//3) (dx)/(1 + sqrt(tan x)) =

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  4. int(-pi)^(pi) (sin^(4)x)/(sin^(4)x+cos^(4)x) dx =

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  5. int(-2)^(2) |x| dx =

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  6. Suppose f is such that f(-x) = -f(x) for all real x and int0^(1) f(x) ...

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  7. int(-1)^(0) (9x^(2)+2x+2 ) dx=

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  8. int(-1)^(1) log (x+sqrt(x^(2)+1))dx =

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  9. If F(x) = int(x^(2))^(x^(3)) log t dt ,( t gt 0) then F^(')(x) is equa...

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  10. int0^(pi) e^(sin^(2)x). cos^(3) x dx =

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  11. The value of int0^(1) (dx)/(x+sqrt(1-x^(2))) dx

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  12. inta^(b) (sqrtx dx)/(sqrtx + sqrt(a+b-x)) =

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  13. The value of int2^(3) (x+1)/(x^(2)(x-1)) dx =

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  14. If g(x) = (f(x)-f(-x))/2 defined over [-3,3] and f(x) = 2x^(2)-4x+1, t...

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  15. int0^(pi/4) (cos x- sin x) dx + int(pi/4)^((5pi)/4) (sinx-cosx) dx + i...

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  16. The value of the integral int0^(oo) log(x+1/x) (dx)/(x^2 +1) is

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  17. If f: R rarr R and g:R rarr R are one-to-one, real valued functions, t...

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  18. If int(log2)^(x) (du)/((e^(u)-1)^(1/2)) = pi/6, then e^(x) =

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  19. The value of int0^(sin^(2)theta) sin^(-1) sqrtphi dphi + int0^(cos^(2)...

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  20. int0^(10pi) |sin x| dx is

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