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Chapter 4: Q. 26 (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.

鈭�-rrr2-x2dx.

Short Answer

Expert verified

The exact value of鈭�-rrr2-x2dxis,蟺谤22.

Step by step solution

01

Step 1. Given information

鈭�-rrr2-x2dx.

02

Step 2. The following figure shows the graph of r2-x2.

03

Step 3. Find the area.

The shaded region can be considered to be a half circle of radius runits.

The area of the shaded half circle is,

A=蟺radius22=蟺谤22

Hence, the exact value is,蟺谤22.

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