Question

4. (Total Area) Find the total area between the region and the x-axis.

y = x³ - 2x² - 8x, −4 ≤ x ≤ 4

Answer 1

Explanation:

You use thr Rienmann integral. Then A=∫3−2(x3−x2−6x)dx=[x4/4−x3/3−3x2]x=3x−2. This is the area with sign. If you want the area without sign: A=∫0−2(x3−x2−6x)dx−∫30(x3−x2−6x)dx. The polynomial is negative in [0,3].