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(MATH100)quiz02-1b.pdf
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MATH 100 (L1) Introduction to Multivariable Calculus Spring 2006-07

. Quiz 02 (April 27, 2007): Multiple Integrals Duration: 40 minutes
Name: ID No.: Tutorial Section: T1B
Answer ALL of the following 4 short answer questions. Show all your work for full credit.

1. (2 Marks) Sketch the solid G whose volume is given by the triple integral
Z 2 Z 1 Z 4.x.y
1 dz dx dy.
000
Answer:
2. (3 Marks) Evaluate the double iterated integral by interchanging the order of integration.
Z 4 Z 23
cos(2y ) dy dx.
0 x
Answer: The iterated integral equals: 3. (2 Marks) Use polar coordinates to evaluate the iterated integral

Z 1 2
1.y
Z
p1 . x2 . y2 dx dy. 00
Answer: The iterated integral equals:
222
4. (3 Marks) Let G be the solid region inside the sphere x + y + z = 6 and above the paraboloid z = x 2 +y 2 . Express the volume of the solid as an iterated triple integral in cylindrical coordinates. You are NOT required to evaluate the triple integral but you have to write the integration limits properly.
Answer: The triple integral is: