16 MULTIPLE INTEGRALS
16 MULTIPLE INTEGRALS
16 MULTIPLE INTEGRALS
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
(b) Evaluate ∫∫ Pac-Man xdAand ∫∫ Pac-Man ydA. 935<br />
CHAPTER <strong>16</strong><br />
SAMPLE EXAM<br />
11. Consider the region R enclosed by y = x + 1, y =−x + 1, and the x-axis.<br />
y<br />
1<br />
R<br />
_1 1<br />
x<br />
(a) Set up the integral ∫∫ R<br />
xydx dy in polar coordinates.<br />
(b) Compute the integral ∫∫ R<br />
xydx dy using any method you know.<br />
12. Consider the double integral<br />
∫∫<br />
1<br />
R 9 − ( x 2 + y 2) 3/2 dA<br />
where R is given by the region between the two semicircles pictured below:<br />
(a) Compute the shaded area.<br />
1<br />
(b) Show that the function<br />
9 − ( x 2 + y 2) 3/2<br />
is constant on each of the two bounding semicircles.<br />
(c) Give a lower bound and an upper bound for the double integral using the above information.<br />
13. Observe the following Pac-Man:<br />
(a) Describe him in polar coordinates.
Change language