Question

Use geometry (i.e., areas of triangles, rectangles, and circles) to find the exact values of each of the definite integrals in Exercises $21-28$.

${\int }_{-3}^{8}24dx$.

Short answer

The exact value of${\int }_{-3}^{8}24dx$is,$264$.

Step-by-step solution

Step 1. Given information

${\int }_{-3}^{8}24dx$.

Step 2. The following figure shows the graph of y=24.

Step 3. Find the area.

The area of the shaded rectangle is,

$$\begin{gathered} l\times b=11\times 24 \\ =264 \end{gathered}$$

Therefore, the exact value is,$264$.