If w=2x, then \int\limits^2_0 {f(2x)} \, dx =

Question

`If w=2x, then \int\limits^2_0 {f(2x)} \, dx =`

Answer 1

First, you should solve for
`f(2x)`, which equals
`2*(2x)=4x`. Now, solve the integral of
`f(2x)`=
`2*(2x)=4x`, to get that
`\int\ {(f(2x)=4x)} \, dx= 2x^2`. You can check this by taking the integral of what you got. Now by the Fundamental Theorem
`\int\limits^2_0 {4x} \, dx=[2x^2] ^(2)_(0)=2(2)^(2)-2(0)^2=8`.

This should be the answer to your question, if I understood what you were asking correctly.