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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.

鈭�-223+4-x2dx.

Short Answer

Expert verified

The exact value of鈭�-223+4-x2dxis,18.283.

Step by step solution

01

Step 1. Given information

鈭�-223+4-x2dx.

02

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

03

Step 3. Find the area.

The area of the shaded half circle and rectangle is,

蟺(2)22+(3脳4)=2蟺+12=18.283

Therefore, the exact value is,18.283.

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Most popular questions from this chapter

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.鈭�x2-3x5-7dx

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals.

Use a graph to check your answer.

鈭�鈭�32鈥�1(x+5)2dx

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

Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) A function f for which the signed area between f and the x-axis on [0, 4] is zero, and a different function g for which the absolute area between g and the x-axis on [0, 4] is zero.

(b) A function f whose signed area on [0, 5] is less than its signed area on [0, 3].

(c) A function f whose average value on [鈭�1, 6] is negative while its average rate of change on the same interval is positive.

Suppose f is positive on (鈭掆垶, 鈭�1] and [2,鈭�) and negative on the interval [鈭�1, 2]. Write (a) the signed area and (b) the absolute area between the graph of f and the x-axis on [鈭�3, 4] in terms of definite integrals that do not involve absolute values.
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