We did a number of examples of substitution. Basic principle: look deep into your complicated function for the smallest substitution you can make.
For example, when integrating 1 / x (ln x)1/2, let u = ln x not (ln x)1/2 or anything more complicated.
6.1 Area between two curves.
6.2 Volume = integral of areas
We set up the integral for computing the volume of a sphere.
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