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Chapter 4: Q. 27 (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.

鈭�03(1-|x-1|)dx.

Short Answer

Expert verified

The exact value of鈭�03(1-|x-1|)dxis,12.

Step by step solution

01

Step 1. Given information

鈭�03(1-|x-1|)dx.

02

Step 2. The following figure shows the graph of (1-|x-1|).

03

Step 3. Find the area.

The area of the shaded triangle is,

12脳1脳2-12脳2脳12=1-12=12

Therefore, the exact value is,12.

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