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Evaluate the following using limit of a ...

Evaluate the following using limit of a sum: `\int_{0}^a` (3x-1) dx

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CHETANA PUBLICATION-Definite integration-Exercise
  1. Prove that \int{0}^(2a) f(x) dx = \int{0}^a [f(x) + f(2a-x)] dx

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

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  3. Evaluate the following using limit of a sum: \int{0}^a (3x-1) dx

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  4. Evaluate the following using limit of a sum: \int{2}^5 (3x-2x^2) dx

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  5. Evaluate the following using limit of a sum: \int{0}^4 (1+e^x) dx

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  6. Evaluate the following using limit of a sum: \int{0}^((pi)/2) cos x dx

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  7. Evaluate the following using limit of a sum: \int{0}^2 (2x+1) dx

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  8. Evaluate the following using limit of a sum: \int{0}^1 (3x^2+2x+1) dx

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  9. Evaluate the following using limit of a sum: \int{2}^5 2^xdx

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

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

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

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

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

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

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

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

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

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

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

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