1. ## Basic Integration

If $\int_1^4\ f(x)dx=6$ , what is the value of $\int_1^4\ f(5-x)dx?$

2. Originally Posted by Sm10389
If $\int_1^4\ f(x)dx=6$ , what is the value of $\int_1^4\ f(x-5)dx?$
Hi

With no other conditions on f, you cannot know

A change of variables u=x-5 leads to

$\int_1^4\ f(x-5)dx = \int_{-4}^{-1}\ f(u)du$

3. Basic u-substitution: $u = 5 - x \Rightarrow \quad du = -dx$
$\begin{array}{c|r|r}
x & 1 & 4 \\
u & { 4} & { 1} \\
\end{array}$

4. Whoops, I wrote it wrong. It is 5-x, if that helps any, but i don't know how to solve it.
I know substitution and changing the boundaries based on the derivatives, but i don't know what to integrate.