
We practice more computations and think about what integrals mean.

In this section we will continue to set-up (and sometimes compute) double and triple integrals and think about what these mean.

### Triangles

It’s important to do a self-check to see if our purported value for an integral is at all plausible.

The region $$ is a triangle with base $$ and height $$, so the area of the region $$ is $$ which is about $$ square units. In other words, which also means that We are claiming that $$ equals $$, which is about $$.

When $$, the value of $$ is sometimes positive, sometimes negative, but at least we know that and this inequality then implies that So $$ is certainly in the ballpark of plausibility.

### Polar coordinates

Again consider the region How does compare to
$$ $$ $ B ]]>$

### Spheres and hemispheres

Again let $$ be the region Set $$ and $$. How does $$ relate to $$?
$$ $$ $ B ]]>$