Chapter 4: Q. 28 (page 353)

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

Short Answer

Expert verified

The exact value of $\int_{- 2}^{2} (3 + \sqrt{4 - x^{2}}) d x$ is, $18.283$ .

Step by step solution

Step 1. Given information

$\int_{- 2}^{2} (3 + \sqrt{4 - x^{2}}) d x$ .

Step 2. The following figure shows the graph of 3+4-x2.

Step 3. Find the area.

The area of the shaded half circle and rectangle is,

$(\frac{π (2)^{2}}{2}) + (3 \times 4) = 2 π + 12 = 18.283$

Therefore, the exact value is, $18.283$ .

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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 $21 - 28$ .
$\int_{- 2}^{2} (3 + \sqrt{4 - x^{2}}) d x$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. The following figure shows the graph of 3+4-x2.

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.∫-223+4-x2dx.

Short Answer

Step by step solution

Step 1. Given information

Step 2. The following figure shows the graph of 3+4-x2.

Step 3. Find the area.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Discrete Mathematics

Statistics

Mechanics Maths

Geometry

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 $21 - 28$ .
$\int_{- 2}^{2} (3 + \sqrt{4 - x^{2}}) d x$ .