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Evaluate: \int{0}^(pi) frac{x tan x}{sec...

Evaluate: `\int_{0}^(pi) frac{x tan x}{sec x + tan x}` dx

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

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  2. Evaluate: \int{0}^(pi)x sin^3 x dx

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  3. Evaluate: \int{0}^(pi) frac{x tan x}{sec x + tan x} dx

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  4. Evaluate the following: \int{-1}^1 frac{1+x^3}{9-x^2} dx

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

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  6. If \int{0}^h frac{1}{2+8x^2} dx = pi/6, then find the value of h.

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  7. Prove that \int{a}^b f(x) dx = \int{a}^b f(a+b-x) dx

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

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  9. Evaluate \int{0}^(pi) frac{x sin x}{1+sin x} dx

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  10. Evaluate \int{0}^(pi) frac{x}{a^2 cos^2 x + b^2 sin^2 x} dx

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  11. Prove that \int{-a}^a f(x) dx = 0, if f(x) is odd function, =2\int{0}...

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

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  13. Evaluate: \int{-a}^a sqrt (frac {a-x}{a+x}) dx

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

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

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

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

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

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

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

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