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

1 Answer
Konstantinos Michailidis
Sep 15, 2015

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#

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