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\int{0}^1 frac{dx}{sqrt (1+x) - sqrt x} ...

`\int_{0}^1` `frac{dx}{sqrt (1+x) - sqrt x} = k/3`, then `k` is equal to......... A) `sqrt 2(2sqrt 2 -2)` B) `(sqrt 2 /3)(2- 2sqrt 2)` C) `frac{sqrt 2(2 sqrt 2 -2)}{3}` D) `4 sqrt 2`

A

`sqrt 2`(2`sqrt 2` -2)

B

(`sqrt 2`/3)(2- 2`sqrt 2`)

C

`frac{`sqrt 2`(2`sqrt 2` -2)}{3}`

D

4`sqrt 2`

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CHETANA PUBLICATION-Definite integration-Exercise
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  9. The value of I=\int{0}^(pi/2) frac{1}{1+cot x} dx is........... A) pi...

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

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

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

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

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

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

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

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

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

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