Question

If f is continuous and (0,4)∫ f(x) dx = -18, how to evaluate (0,2)∫ f(2x) dx ?

Answer 1

Refer to explanation

Explanation:

Assuming that you mean that

`int_0^4 f(x)dx=-18`

and you want to evaluate `int_0^2 f(2x)dx`

set `u=2x` hence `du=2dx` and

`int_0^2 f(x)dx=int_0^4 (1/2)*f(u)du=(1/2)*int_0^4f(u)du=(1/2)*(-18)=-9`