Question

1. Consider the region bounded by the curves y=|x^2+x-12|, x=-5, and x=5 and the x-axis.

A. Set up a sum of integrals, not containing an absolute value symbol, that can be used to find the area of this region.

B. Find the area of the region by using your answer from part A. Don’t approximate with your calculator.

Answer 1

Since y < 0 for -4 < x < 3,

∫[-4,-4] y dx + ∫[-4,3] -y dx + ∫[3,5] y dx

Now just plug in the polynomial for y, and evaluate each integral.