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Chapter 4: Q. 21 (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�02(2-x)dx.

Short Answer

Expert verified

The exact value of鈭�02(2-x)dxis,2.

Step by step solution

01

Step 1. Given information

鈭�02(2-x)dx.

02

Step 2. The following figure shows the graph of 2-x.

03

Step 3. Find the area.

The area of the shaded region is,

12脳2脳2=2

Therefore, the exact value is,2.

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Most popular questions from this chapter

If 鈭�-23f(x)dx=4,鈭�-26f(x)dx=9,鈭�-23g(x)dx=2and 鈭�36g(x)dx=3,then find the values of each definite integral in Exercises 29-40. If there is not enough information, explain why.

鈭�36fxdx.

Show by exhibiting a counterexample that, in general, 鈭�f(x)g(x)dx鈮�鈭�f(x)dx鈭�g(x)dx. In other words, find two functions f and g so that the integral of their product is not equal to the product of their integrals.

Verify that鈭�cotxdx=ln(sinx)+C. (Do not try to solve the integral from scratch.)

Describe the intervals on which the function f is positive, negative, increasing and decreasing. Them describe the intervals on which the function A is positive , negative, increasing and decreasing

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: tanx=sinxcosx).

鈭�2xlnx-xlnx2dx.
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