Summary: Math 213-001 201130
Assignment # 7 - Sample answers
1. Find the area of the part of the plane 2x + 5y + z = 10 that lies inside
the cylinder x2
+ y2
= 9.
Answer. We integrate inside the disk D = {(x, y) : x2
+ y2
9}.
The plane is z = f(x, y) = 10 - 2x - 5y. Then, using the surface-area
formula,
Area =
D
1 + (-2)2 + (-5)2 dA =
D

30 dA = 9

30.
2. Calculate

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

Collections: Mathematics