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

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

A

(a) `(pi (b-a)^2)`/8

B

(b) `(pi (b+a)^2)`/8

C

(c) `(pi (b-a)^2)`

D

(d) `(pi (b+a)^2)`

Text Solution

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CHETANA PUBLICATION-Definite integration-Exercise
  1. \int{0}^(pi^2/4) sin sqrt x dx =.........

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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