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Definite Integrals: Study Guide

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Definite Integrals: Study Guide
5128_Ch07_pp378-433.qxd 1/13/06 1:13 PM Page 378

Chapter

7

Applications of
Definite Integrals

T

he art of pottery developed independently in many ancient civilizations and still exists in modern times. The desired shape of the side of a pottery vase can be described by: y ϭ 5.0 ϩ 2 sin (x/4) (0 Յ x Յ 8p) where x is the height and y is the radius at height x (in inches).
A base for the vase is preformed and placed on a potter’s wheel. How much clay should be added to the base to form this vase if the inside radius is always 1 inch less than the outside radius? Section 7.3 contains the needed mathematics.

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5128_Ch07_pp378-433.qxd 1/13/06 1:13 PM Page 379

Section 7.1 Integral as Net Change

379

Chapter …show more content…
1156.5
28. Writing to Learn As a school project, Anna accompanies her mother on a trip to the grocery store and keeps a log of the car’s speed at 10-second intervals. Explain how she can use the data to estimate the distance from her home to the store. What is the connection between this process and the definite integral?

See page 389.

29. Hooke’s Law A certain spring requires a force of 6 N to stretch it 3 cm beyond its natural length.

(a) What force would be required to stretch the string 9 cm beyond its natural length? 18 N
(b) What would be the work done in stretching the string 9 cm beyond its natural length? 81 N и cm
30. Hooke’s Law Hooke’s Law also applies to compressing springs; that is, it requires a force of kx to compress a spring a distance x from its natural length. Suppose a 10,000-lb force compressed a spring from its natural length of 12 inches to a length of 11 inches.
How much work was done in compressing the spring
(a) the first half-inch?

(b) the second
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