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

1 Answer

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