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Math Help - Basic Integration

  1. #1
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    Basic Integration

    If \int_1^4\ f(x)dx=6 , what is the value of \int_1^4\ f(5-x)dx?
    Last edited by Sm10389; December 12th 2008 at 08:27 AM.
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  2. #2
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    Quote Originally Posted by Sm10389 View Post
    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
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  3. #3
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    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}
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  4. #4
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    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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