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.

${\int }_0^{\frac{\mathrm{\pi }}{2}}\sin xdx$

Short answer

(a) The integral ${\int }_0^{\frac{\mathrm{\pi }}{2}}\sin xdx$represents the area under the curve $\sin x.$

(b)

(c) area is$1$.

Step-by-step solution

Part (a) Step 1. Given

${\int }_0^{\frac{\mathrm{\pi }}{2}}\sin xdx$

Part (a) Step 2. Calculation

The integral${\int }_0^{\frac{\mathrm{\pi }}{2}}\sin xdx$ represents the area under the curve$\sin x.$

Part (b) Step 1. Graph

Part (c) Step 1. Area Calculation

Using the graphing utility the area is

${\int }_0^{\frac{\mathrm{\pi }}{2}}\sin xdx=1$