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The value of \int{0}^(pi) frac{x}{4 cos^...

The value of `\int_{0}^(pi)` `frac{x}{4 cos^2 x + 9 sin^2 x}` dx is...........

A

(a) `frac{pi^2}{12}`

B

(b)`frac{pi^2}{4}`

C

(c) `frac{pi^2}{6}`

D

(d)`frac{pi^2}{3}`

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CHETANA PUBLICATION-Definite integration-Exercise
  1. The value of \int{-pi/4}^(pi/4) log( frac{2+sin theta }{2-sin theta}) ...

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  2. The value of I=\int{0}^(pi/2) frac{1}{1+cot x} dx is........... A) pi...

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  3. The value of \int{0}^(pi) frac{x}{4 cos^2 x + 9 sin^2 x} dx is...........

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  4. The value of \int{0}^1 x(1-x)^99 dx is........... A) 1/10100 B) 11/1...

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  5. The value of \int{-pi/2}^(pi/2) x sqrt (cos x - cos^2 x) dx is...........

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  6. The value of\int{0}^(pi/2) frac{1}{1+tan^3 x} dx is........... A) 0 B...

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  7. The value of \int{- pi }^(2 pi ) log(sec theta - tan theta ) d theta...

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  8. The value of I= \int{0}^43^(sqrt (2x+1)) is...........

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  9. \int{0}^oo frac{1}{(x^2+4)(x^2+9)}dx=................ (A) pi/30 (B) ...

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  10. \int{0}^((pi)/4) frac{sin x + cos x}{3+ sin 2x}dx =................ (...

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  11. \int{pi/4}^((3pi)/4) frac{1}{1+ cos x}dx=................

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  12. \int{0}^(pi^2/4) sin sqrt x dx =.........

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  13. \int{0}^((pi)/4) log(1+2tantheta + tan^2theta) dtheta =.........

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  14. \int{a}^b sqrt ((x-a)(b-x)) dx is equal to........

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  15. \int{0}^((pi)/2) sqrt sin2 theta sin theta dtheta is .........

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  16. \int{-2}^2 abs(1-x) dx=...........

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

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

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

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

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