1. ## integrate

if f is continuous and integrating from 0 to 4 f(x)dx =10 find what integrating from 0 to 2 f(2x)dx is

2. ## Re: integrate

Originally Posted by pnfuller
if f is continuous and integrating from 0 to 4 f(x)dx =10 find what integrating from 0 to 2 f(2x)dx is

Let $u=2x~\&~du=2dx$ so $\begin{array}{*{20}c} x &\vline & 0 &\vline & 2 \\\hline u &\vline & 0 &\vline & 4 \\ \end{array}$.

So $\int_0^2 {2f(2x)dx} = \int_0^4 {f(u)du}$

3. ## Re: integrate

wouldn't it be 1/2f(2x) and do you have to do anything else to solve for what it equals like f(x)=10 in the first part, how do you find what f(2x) equals?

4. ## Re: integrate

Originally Posted by pnfuller
wouldn't it be 1/2f(2x) and do you have to do anything else to solve for what it equals like f(x)=10 in the first part, how do you find what f(2x) equals?

Why don't you try this for yourself?

The is simple algebra, $\int_0^2 {2f(2x)dx} = \int_0^2 {f(2x)\left( {2dx} \right)}$.

If $\int_a^b {f(t)dt} = C$ THEN $\int_{u(a)}^{u(b)} {f(u)du} = C$