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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. \int{2}^a[1/log x - 1/(log x)^2] dx = a + b/ log 2 A) a=e, b=-2 B) ...

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  18. Let I1= \int{e}^ {e^2} dx/log x and I2= \int{1}^2 frac{e^x}{x} dx, th...

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  19. \int{0}^9 frac{sqrt x}{ sqrt x + sqrt (9-x)} dx=............. A) 9/2 B...

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  20. The value of \int{-pi/4}^(pi/4) log( frac{2+sin theta }{2-sin theta}) ...

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