Return to Assignments Integration by substitution
Assignment 4
Solve:
Solution
We use the transform:
and get:
or:
We are not ready yet. There are boundaries from 
to 
. These boundaries hold for the variable 
and thus they have to be transformed as well in 
. Thus the transformed boundaries are from 
to 
. As a result we get the following integral:
![\displaystyle\int_{7}^{10}{\displaystyle\frac{1}{u}\cdot\displaystyle\frac{1}{3}}du=\displaystyle\frac{1}{3}[\ln(|u|)]_{7}^{10}=\displaystyle\frac{1}{3}[\ln(10)-\ln(7)]=\displaystyle\frac{1}{3}\ln(\displaystyle\frac{10}{7})](https://4mules.nl/wp-content/ql-cache/quicklatex.com-339b78b97fac823c3c9bebbde9ab2da8_l3.png "Rendered by QuickLaTeX.com")
We can verify whether the primitive function is correct by differentiation. The chain rule has to be applied.
Return to Assignments Integration by substitution
