Overview
I'm working on a mathematics multi-part question and need an explanation and answer to help me learn.
To find the area enclosed, we integrate over the three separate regions, from ?2 to ?1, from ?1 to 1, and from 1 to 2: Z ?1 ?2 x 2 ? 1 dx = 1 3 x 3 ? x ?1 ?2 = (? 1 3 + 1) ? (? 8 3 + 2) = 4 3 Z 1 ?1 x 2 ? 1 dx = 1 3 x 3 ? x 1 ?1 = ( 1 3 ? 1) ? (? 1 3 + 1) = ? 4 3 Z 2 1 x 2 ? 1 dx = 1 3 x 3 ? x 2 1 = ( 8 3 ? 2) ? ( 1 3 ? 1) = 4 3The graph is of y = x 2 ? 1 = (x + 1)(x ? 1), so the parabola intersects the x-axis at (1, 0) and (?1, 0):