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Prove that int0^(2a) f(x)/(f(x)+f(2a-x))...

Prove that `int_0^(2a) f(x)/(f(x)+f(2a-x))dx=a`

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Prove that int_(a)^(b)(f(x))/(f(x)+f(a+b-x)) dx=(b-a)/(2) .

If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove that int_0^(2a)f(x)dx=int_0^a{f(x)+(2a-x)}dx

Knowledge Check

  • int_(0)^(a)(f(x))/(f(x)+f(a-x))dx=

    A
    `(a)/(2)`
    B
    2a
    C
    a
    D
    3a

  • The value of the integral int_(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal to

    A
    0
    B
    2a
    C
    a
    D
    none of these

  • int_(0)^(a) (f(a+x) + f(a-x) ) dx =

    A
    `2int_(0)^(2a) f(x) dx`
    B
    `int_(0) ^(2a) f(x) dx`
    C
    `2int_(0) ^(a) f(x) dx`
    D
    `int_(0) ^(a) f(x) dx`

    • Similar Questions

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    Prove that int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx

    If f(2a-x)=-f(x), prove that int_0^(2a)f(x)dx=0

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