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\int{0}^((pi)/2)frac{sin^2 x dx}{(1+cos ...

`\int_{0}^((pi)/2)``frac{sin^2 x dx}{(1+cos x)^2}`=........... A) `frac{4-pi}{2}` B) `frac{pi-4}{2}` C) `4- frac{pi}{2}` D) `frac{4+pi}{2}`

A

`frac{4-`pi`}{2}`

B

`frac{`pi`-4}{2}`

C

4- `frac{`pi`}{2}`

D

`frac{4+`pi`}{2}`

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CHETANA PUBLICATION-Definite integration-Exercise
  1. Evaluate: \int{0}^((pi)/2) cos^2 x dx

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  2. \int{2}^3 frac{dx}{x(x^3 -1)}=.............. (A) 1/3 log(208/189) (B)...

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  3. \int{0}^((pi)/2)frac{sin^2 x dx}{(1+cos x)^2}=........... A) frac{4-p...

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  4. \int{0}^log 5 frac{e^x sqrt (e^x -1)}{e^x + 3} dx=........... A) 3+2p...

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  5. \int{0}^((pi)/2) sin^6 x cos^2 x dx=............. (A) frac{7pi}{256} ...

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  6. \int{0}^1 frac{dx}{sqrt (1+x) - sqrt x} = k/3, then k is equal to........

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  7. \int{1}^2 frac{1}{x^2} e^(1/x) dx =................ A) sqrt e +1 B) s...

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  8. \int{2}^a[1/log x - 1/(log x)^2] dx = a + b/ log 2 A) a=e, b=-2 B) ...

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  9. Let I1= \int{e}^ {e^2} dx/log x and I2= \int{1}^2 frac{e^x}{x} dx, th...

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  10. \int{0}^9 frac{sqrt x}{ sqrt x + sqrt (9-x)} dx=............. A) 9/2 B...

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

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

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

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

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

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

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

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

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

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

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