9 FURTHER APPLICATIONS OF INTEGRATION

9.3 APPLICATIONS TO PHYSICS AND ENGINEERING
SUGGESTED TIME AND EMPHASIS
1
2
–1 class Optional material
POINTS TO STRESS
1. Two applications (hydrostatic pressure; moments and centers of mass) are discussed in the text. It is
recommended that the instructor stress one, and perhaps touch on the other.
2. Centroids and the symmetry principle, if moments and centers of mass are covered.
QUIZ QUESTIONS
• Text Question: Both applications in the text start by a summation of discrete or sampled data, and
eventually replace the summation by an integral. We have seen this technique earlier in the course. Name
two previous occasions where we’ve used the technique of changing the sum of sample values into an
integral of a continuous function.
Answer: Answers include finding the area under a curve, finding average values of a function, and finding
volumes.
• Drill Question: Set up, but do not evaluate, an integral or integrals that will give the y-coordinate of the
centroid of the region sketched below.
y
4
3
y=4-x@
2
1
_2 _1 0 1 2 x
_1
Answer: y =
∫ 2
−2 1 2
( 4 − x
2 ) 2 dx
∫ 2 (
−2 4 − x 2 ) dx
MATERIALS FOR LECTURE AND WORKSHOP/DISCUSSION
Lecture coverage will, of course, be determined by which applications are to be emphasized. I recommend
an in-depth treatment of one of the two applications in lecture, and touching on the other in discussion.
Throughout, emphasize problem solving skills such as drawing a picture and setting up the problem carefully.
• Hydrostatic Pressure and Force: Work through Exercise 14. This problem requires resolving a force on a
dam with inclined sides.
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