Question

Find the area between the curves on the given interval. y = x3, y = x2 – 1, 1 ≤ x ≤ 3

Answer 1

You have \[\color{#0088AA}{y=x^{3}} , \color{#991188}{y=x ^{2}-1}\] do you know what the graph of a cubic function and a parabola looks like?

Answer 2

For \(x\in[1,3]\), you have \(x^3\ge x^2-1\), so the integral representing the area is
\[A=\int_1^3\left(x^3-(x^2-1)\right)~dx\]