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.

${\int }_0^{4}16-x^{2}dx$

Short answer

(a) The integral ${\int }_0^{4}16-x^{2}dx$represents the area under the curve $16-x^2$.

(b)

(c) area is$\frac{128}{3}$.

Step-by-step solution

Part (a) Step 1. Given

${\int }_0^{4}16-x^{2}dx$

Part (a) Step 2. Calculation

The integral${\int }_0^{4}16-x^{2}dx$ represents the area under the curve$16-x^2$.

Part (b) Step 1. Graph

Part (c) Step 1. Area Calculation

Using the graphing utility the area is

${\int }_0^{4}16-x^{2}dx=\frac{128}{3}$