Test 1 Review Answers
Math 214 Spring 2001
1) Page 471 #2
The integral is = 16 1/5 = 81/5
2) Page 471 #16
Horizontal is obviously easier. Compute to get area = 4/3
3) Page 471 #22
a) Discs: = 8p
b) Shell: Note: This is the same integral as part (a) if you
set (a) up using shells.
Discs were easier here.
4) Page 472 #41
Draw the picture so the bottom of the well is centered about the origin, then
all the numbers are positive. For a representative disc, or cylinder:
where r = 1/3
the distance the disc must be lifted is 175 – y feet. So,
5) Page 472 #46
Notice that the area under the curve has the units of (pounds)(feet) = ft-lbs which
are the units for work. So, find the area under the curve:
Between 0 and 9 the curve is the straight line y = -2/9 x + 6
Between 9 and 12, the curve is the line y = -4/3 x + 16
Do the integration to get the total area : 45 + 6 = 51
6) Page 472 #48
The centroid is just the center of mass for an object of constant density. Recall
that r always cancels in the division when it is constant.
Need mass = = 32/3
Moment about the x-axis: = 544/15
Moment about the y-axis: = 32/3
This results in: I hope.