Q. 24 - Calculus

Question

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

${\int }_{-2}^4|3x+1|dx$.

Step-by-Step Solution

Answer

The exact value of ${\int }_{-2}^4|3x+1|dx$ is, $28.97$.

Step 1 . Given information

${\int }_{-2}^4|3x+1|dx$.

Step 2 . The following figure shows the graph of 3 x + 1 .

Step 3 . Find the area.

The area of the shaded triangles is,

$$\begin{gathered} \left(\frac{1}{2}\times 0.33\times 5\right)+\left(\frac{1}{2}\times 13\times 4.33\right)=0.825+28.145 \\ =28.97 \end{gathered}$$

Therefore, the exact value is, $28.97$.