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Worksheet 16 1.) Find the area of the region bounded by the graphs of 9 = 1: /6 ,
e=n/4,and r=sec9. 2.) Find the area of the region lying inside the graph of r = 2 + sin 9 and
outside thegraph of r = cos 9. 3.) Find the area of the region lying inside the graph of r=Ll sin 8 and
above the graph of r = csc 9. 4.) Find the area of one leaf of the graph of a.) r=sin29
b.) r=sin39 5.) Find all points of intersection (in polar coordinates) of the following
pairs of polar equations. Begin by sketching the graph of each equation. ln
part f.) a good estimate of the point(s) of intersection will do. .) 9=1c/3,r=1+1/zcose
.) r=1/2,r=cose .) r=sine,r=\l§'cose .) r=1—sin9,r=sin9 .) r=1+sin9,r=csc9
.) r=9,l'=3S'm9 (DQOU‘CD —o. 1
(Lose-+1 6.) Sketch the graph of r = . What is it? 7.) Sketch the graph of r =1/9 for 0 < 9 g 2 1c. 8.) Considera flat, spinning circular disc of mass M and radius a and
constant density . It rotates about an axis perpendicular to its face and
passing through its center f times per second. a.) Calculate the total kinetic energy of the spinnig disc.
b.) Assume that the disc (while spinning) starts to deteriorate and " spin off " thin slices until the disc is gone ? Find the total kinetic
energy of these slices if each slice is " dr " thick and " 2m " long. What
happens to the total kinetic energy ? :_ ;\ 3r cl r‘
-—-—3 9.) Determine whether the following improper integrals are convergent
or divergent. 00 l a.) 83 X-3 M
:2 2X b.) 80 xa—t obx ...
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- Spring '07