# How do you change bounds when you integrate by substitution method?

Apr 1, 2015

Use the substitution you made and arithmetic.

For ${\int}_{1}^{4} {\left(5 - 3 x\right)}^{4} \mathrm{dx}$

You'll substitute $u = 5 - 3 x$ which makes $\mathrm{du} = - 3 \mathrm{dx}$ and $\mathrm{dx} = - \frac{1}{3} \mathrm{du}$

It also makes the lower limit of integration: $5 - 3 \left(1\right) = 2$ (When $x = 1$, $u = 2$

And the upper limit of integration becomes $5 - 3 \left(4\right) = - 7$.

With these substitutions, we now need to find:

$- \frac{1}{3} {\int}_{2}^{- 7} {u}^{4} \mathrm{du}$
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