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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.

鈭�-24|3x+1|dx.

Short Answer

Expert verified

The exact value of鈭�-24|3x+1|dxis,28.97.

Step by step solution

01

Step 1. Given information

鈭�-24|3x+1|dx.

02

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

03

Step 3. Find the area.

The area of the shaded triangles is,

12脳0.33脳5+12脳13脳4.33=0.825+28.145=28.97

Therefore, the exact value is,28.97.

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Most popular questions from this chapter

Write out all the integration formulas and rules that we know at this point.

Prove that 鈭�13(3x+4)dx=20in three different ways:

(a) algebraically, by calculating a limit of Riemann sums;

(b) geometrically, by recognizing the region in question as a trapezoid and calculating its area;

(c) with formulas, by using properties and formulas of definite integrals.

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