Question

(a) What area does the integral represent?

(b) Provide a graph that illustrates this area.

(c) Use a graphing utility to approximate this area.

${\int }_2^5\left(x^2-1\right)dx$

Short answer

(a) The integral ${\int }_2^5\left(x^2-1\right)dx$represents the area under the curve $\left(x^2-1\right)$.

(b)

(c) area is$36$.

Step-by-step solution

Part (a) Step 1. Given

${\int }_2^5\left(x^2-1\right)dx$

Part (a) Step 2. Calculation

The integral${\int }_2^5\left(x^2-1\right)dx$ represents the area under the curve$x^2-1$.

Part (b) Step 1. Graph

Part (c) Step 1. Area Calculation

Using the graphing utility the area is

${\int }_2^5\left(x^2-1\right)dx=36$