Basic Integration

**Sm10389** · December 12th 2008, 08:13 AM

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

**running-gag** · December 12th 2008, 08:24 AM

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

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

**Plato** · December 12th 2008, 08:27 AM

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

**Sm10389** · December 12th 2008, 08:27 AM

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.

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