Problem #6-1-23, with solution suggested by Mark Cate.

Here is the problem: find the area bounded by the -axis and the curve .

Solution: switch and and find the area between the -axis and the curve .

The zeros of this function can be found by factoring (by grouping):

, so the zeros are at .

We have two regions. We'll integrate and evaluate each region separately using absolute values.

+
+

Oh heck, I'll let Mathematica do it.

Taking absolute values gives

The textbook has 331/4, which appears to be a typo. Notice that which is bigger than 80 which is 16×5, which is the area of a box that bounds both regions. So that can't be right.