Question

If f(2a – x) = f(x), then `int_0^(2a)f(x)  dx` is ______.

Options

• `int_0^(2a)f(x/2) dx`

• `int_0^a f(x) dx`

• `2int_a^0 f(x) dx`

• `2int_0^a f(x) dx`

Answer 1

If f(2a – x) = f(x), then `int_0^(2a)f(x)  dx` is `bbunderline(2int_0^a f(x) dx)`.

Explanation:

Using the property,

`int_0^(2a)f(x) dx = {(2int_0^a f(x) dx",", if f(2a - x) = f(x)),(                            0",", if f(2a - x) = -f(x)):}`

`int_0^(2a)f(x) dx = 2int_0^a f(x) dx`