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

Prove that `\int_{a}^b` f(x) dx = `\int_{a}^b` f(t) dt

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

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

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  3. Prove that \int{a}^b f(x) dx = \int{a}^b f(t) dt

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  4. Prove that \int{a}^b f(x) dx = \int{a}^c f(x) dx + \int{c}^b f(x) dx, ...

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

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  6. Prove that \int{0}^a f(x) dx = \int{0}^a f(a-x) dx

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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