Find the total area between y = x³ − x and the x-axis from x = −1 to x = 1.

Question

G1 Physics · Accepted Answer

The roots are −1, 0, 1. The function is odd, so the two geometric parts are equal. For 0<x<1, x³−x<0. Area = 2∫₀¹(x−x³)dx = 2[x²/2−x⁴/4]₀¹ = 2(1/4) = 1/2 square unit.