Chapter 4: Q. 24 (page 352)

Use geometry (i.e., areas of triangles, rectangles, and circles) to find the exact values of each of the definite integrals in Exercises $21 - 28$ .
$\int_{- 2}^{4} | 3 x + 1 | d x$ .

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

$\int_{- 2}^{4} | 3 x + 1 | d x$ .

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

Step 3. Find the area.

The area of the shaded triangles is,

$(\frac{1}{2} \times 0.33 \times 5) + (\frac{1}{2} \times 13 \times 4.33) = 0.825 + 28.145 = 28.97$

Therefore, the exact value is, $28.97$ .

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Use geometry (i.e., areas of triangles, rectangles, and circles) to find the exact values of each of the definite integrals in Exercises $21 - 28$ .
$\int_{- 2}^{4} | 3 x + 1 | d x$ .

Short Answer

Step by step solution

Step 1. Given information

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

Step 3. Find the area.

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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.∫-24|3x+1|dx.

Short Answer

Step by step solution

Step 1. Given information

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

Step 3. Find the area.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Mechanics Maths

Calculus

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use geometry (i.e., areas of triangles, rectangles, and circles) to find the exact values of each of the definite integrals in Exercises $21 - 28$ .
$\int_{- 2}^{4} | 3 x + 1 | d x$ .