Given $$\int\limits_{0}^{4}f(x)dx=8$$. Find $$\int\limits_{0}^{12}(2f(3x)-x)dx$$.

I don't know how should i do this question. Can someone help me out.

Thanks.

Question

Given $$\int\limits_{0}^{4}f(x)dx=8$$. Find $$\int\limits_{0}^{12}(2f(3x)-x)dx$$.

I don't know how should i do this question. Can someone help me out.

Thanks.

kainui · Answer

What have you tried? Play around with it with some algebra a little bit and show me what you get.

rahulmr · Answer

$$2\int\limits_{0}^{12}f(3x)dx-\int\limits_{0}^{12}(x)dx$$
I don't know what to do next.

loser66 · Answer

the second one is ok, right? 
Now the first one
you need find 
$$2\int_0^{12} f(3x) dx$$

Let u =3x, du /3 =dx
x= 0 , u =0
x=12 u =4, then you have \
$$2\int_0^4 f(u) du =2*8$$

Don't forget + the second part

rahulmr · Answer

Thanks, But how can i get rid of the 3 when i'll sub the 3x back into the equation

jim_thompson5910 · Answer

if x = 12, then u = 3x = 3*12 = 36

loser66 · Answer

oh yeah!! my bad!! I am so sorry
Thank you so much @Mr. Jim :)

loser66 · Answer

I should go to bed now. :)

rahulmr · Answer

Okay. Thanks for the help

jim_thompson5910 · Answer

Are you sure the 3x is there? If it was x/3, then it would work. I'm thinking there's a typo somewhere.