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

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- Dec 12th 2008, 08:13 AMSm10389Basic Integration
If $\displaystyle \int_1^4\ f(x)dx=6$ , what is the value of $\displaystyle \int_1^4\ f(5-x)dx?$

- Dec 12th 2008, 08:24 AMrunning-gag
- Dec 12th 2008, 08:27 AMPlato
Basic u-substitution: $\displaystyle u = 5 - x \Rightarrow \quad du = -dx$

$\displaystyle \begin{array}{c|r|r}

x & 1 & 4 \\

u & { 4} & { 1} \\

\end{array} $ - Dec 12th 2008, 08:27 AMSm10389
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.