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Evaluate the following: If \int{0}^a sqr...

Evaluate the following: If `\int_{0}^a` `sqrt x` dx = 2a `\int_{0}^((pi)/2)` `sin^3` x dx,
find the value of `\int_{a}^(a+1)` x dx.

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CHETANA PUBLICATION-Definite integration-Exercise
  1. Evaluate the following: If \int{0}^a sqrt x dx = 2a \int{0}^((pi)/2) s...

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  2. Evaluate the following integrals as a limit of the sum: \int{1}^2 (2x+...

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  3. Evaluate the following integrals as a limit of sum: \int{2}^37^x dx

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  4. Evaluate the following integrals as a limit of sum: \int{0}^4(x- x^2) ...

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  5. Evaluate the following integrals as a limit of sum: \int{0}^((pi)/2)si...

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  6. Evaluate the following integrals as a limit of sum: \int{0}^2 (2x+1) d...

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  7. Evaluate the following integrals as a limit of sum: \int{3}^5 (2 - x) ...

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  8. Evaluate the following integrals as a limit of sum: \int{0}^13^x dx

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  9. Evaluate the following integrals as a limit of sum: \int{0}^3(x+4) dx

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  10. Evaluate the following integrals as a limit of sum: \int{0}^3(e^x+ 6 x...

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  11. Evaluate the following integrals as a limit of sum: \int{1}^3a^x dx

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  12. Evaluate the following definite integrals: \int{(pi)/6}^((pi)/3) sin^2...

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  13. Evaluate the following definite integrals:\int{0}^((pi)/4)log(1+ tanx)...

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  14. Evaluate the following definite integrals: \int{(-pi)/4}^((pi)/4) x^3 ...

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  15. Evaluate the following definite integrals: \int{-pi/4}^((pi)/4) frac{x...

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  16. Evaluate the following definite integrals: \int{1}^2 frac{log x}{x^2} ...

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  17. Evaluate the following definite integrals:\int{0}^((pi)/2) frac{cos x}...

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  18. Evaluate the following definite integrals: \int{0}^(1/2) frac{1}{(1-2x...

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  19. Evaluate the following definite integrals: \int{-1}^1 abs(5x-3) dx

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  20. Evaluate the following definite integrals:\int{0}^((pi)/2) frac{1}{1+r...

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  21. Evaluate the following definite integrals: \int{3}^8 frac{(11-x)^2}{x^...

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