If $\displaystyle \int_1^4\ f(x)dx=6$ , what is the value of $\displaystyle \int_1^4\ f(5-x)dx?$
Last edited by Sm10389; Dec 12th 2008 at 08:27 AM.
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Originally Posted by Sm10389 If $\displaystyle \int_1^4\ f(x)dx=6$ , what is the value of $\displaystyle \int_1^4\ f(x-5)dx?$ Hi With no other conditions on f, you cannot know A change of variables u=x-5 leads to $\displaystyle \int_1^4\ f(x-5)dx = \int_{-4}^{-1}\ f(u)du$
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} $
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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