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Evaluate the following: \int{0}^(pi /4) ...

Evaluate the following: `\int_{0}^(pi /4) frac{tan^3 x}{1+ cos 2x}` dx

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

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  2. Evaluate: \int{0}^afrac{dx}{a^2+ax-x^2}

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  3. Evaluate the following: \int{0}^(pi /4) frac{tan^3 x}{1+ cos 2x} dx

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  4. Evaluate: \int{(pi )/4}^(( pi )/2) frac{cos theta }{cos ( theta /2) ...

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  5. Evaluate: \int{2}^4 frac{x^2 + x}{sqrt (2x+1)} dx

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

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  7. Evaluate the following: \int{0}^((pi)/2) frac{cos x}{3cos x + sin x} d...

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  8. Evaluate: \int{0}^(pi/2) (2 log sinx - log sin 2x) dx

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

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

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

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

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

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

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

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

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

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

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

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

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