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Show that int0^a f(x)g(x)dx = 2 int0^a f...

Show that `int_0^a f(x)g(x)dx = 2 int_0^a f(x)dx`, if f and g are defined as `f(x) = f(a-x)` and `g(x) + g(a-x) = 4`

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PRADEEP PUBLICATION-INTEGRALS-EXERCISE
  1. Evaluate the following integrals: underset(0)overset(a)int(sqrtx)/(s...

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  2. Evaluate the integrals underset0overset4int |x-1|dx

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  3. Show that int0^a f(x)g(x)dx = 2 int0^a f(x)dx, if f and g are defined ...

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  4. The value of int(-pi//2)^(pi//2) (x^3+xcosx+tan^5x+1)dx is :

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  5. The value of int(0)^(pi//2)log((4+3sinx)/(4+3cos x))dx is

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  6. Integrate the function: 1/(x-x^3)

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  7. Integrate the function: 1/(sqrt(x+a)+sqrt(x+b))

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  8. Evaluate the following integrals : int(dx)/(xsqrt(ax-x^2))

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  9. Integrate the following functions w.r.t. x, 1/(x^2(x^4+1)^(3/4))

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  10. Integrate the following functions w.r.t. x, 1/x^(1/2)+x^(1/3)

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  11. Integrate the following functions w.r.t. x, 1/(x^2(x^4+1)^(3/4))

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  12. Integrate the following functions w.r.t. x, (sinx)/(sin(x-a)

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  13. Integrate the function: (e^(5logx) - e^(4logx))/(e^(3logx)-e^(2logx))

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  14. Integrate the following functions w.r.t. x, (cosx)/(sqrt(4-sin^2x))

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  15. Integrate the following functions w.r.t. x, (sin^8-cos^8x)/(1-2sin^2xc...

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  16. Compute the following integrals: int(1)/(cos(x+a)cos(x+b))dx

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  17. Integrate the following functions w.r.t. x, x^3/sqrt(1-x^8)

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  18. Integrate the following functions w.r.t. x, e^x/((1+e^x)(2+e^x))

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  19. Integrate the function: 1/((x^2+1)(x^2+4))

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  20. Differentiate the following functions w.r.t.x : e^x cos^3 x sin^4 x

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