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The value of integral \int{(-pi)/3}^((pi...

The value of integral `\int_{(-pi)/3}^((pi)/3)` `frac{x sin x}{cos^2 x}` dx is...........

A

(a) `frac{pi}{3} - log tan (frac{3pi}{2})`

B

(b) `2(frac{2 pi}{3}) - log (2+ frac{sqrt 3}{2})`

C

(c) `frac{pi}{2} - log tan (frac{pi}{12})`

D

(d) `2 (frac{2 pi} {3}) +2 log (2- sqrt 3)`

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CHETANA PUBLICATION-Definite integration-Exercise
  1. \int{-2}^2 abs(1-x) dx=...........

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  2. The value of \int{0}^(oo) frac{x log x}{(1+x^2)^2} dx is ...........

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  3. The value of integral \int{(-pi)/3}^((pi)/3) frac{x sin x}{cos^2 x} dx...

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  4. \int{0}^1 tan^(-1) frac{x}{sqrt (1-x^2)} dx is.......... A) (pi)/2 +1...

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  5. \int{0}^((pi)/4) frac{sin 2t}{sin^4 t + cos^4 t} dt is..........

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  6. \int{2}^3 frac{1}{x ( x^2 -1)} dx is.......... A) (1/2) log (32/27) ...

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  7. \int{0}^1 x^2 sqrt(1-x) dx is..........

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  8. \int{0}^pi frac{t tan t}{sec t + cos t} dt =..........

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  9. \int{0}^((pi)/2) frac{sin x}{(sin x + cos x)^2} dx =k log(1+sqrt 2), ...

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  10. \int{0}^(pi/2) sin(x-(pi)/4) dx =......... A) 2+sqrt 2 B) 2-sqrt 2 ...

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  11. If \int{0}^k 4x^3 dx =16, then value of k is .......... A) 1 B) 2 C)...

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  12. If \int{0}^1 frac{dx}{sqrt (1+x) -sqrt x} = k/3, then k=...........

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  13. The value of \int{-pi/4}^(pi/4) log( frac{2+sin theta }{2-sin theta}) ...

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  14. If \int{0}^k 4x^3 dx =16, then value of k is .......... A) 1 B) 2 C)...

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  15. Evaluate the following: If \int{0}^k frac{1}{2+8x^2} dx = (pi)/16, fin...

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  16. Evaluate : \int{1}^2 frac{1}{x^2} e^(1/x) dx

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  17. Evaluate: \int{0}^((pi)/4) frac{tan^3 x}{1+ cos 2x} dx

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  18. Evaluate: \int{0}^1frac{x^2 - 2}{x^2+1} dx

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  19. Evaluate: \int{0}^((pi)/2) x sinx dx

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  20. Prove that \int{0}^(2a) f(x) dx = \int{0}^a [f(x) + f(2a-x)] dx

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