This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 2 and the region R is between the circle of
radius 1 and 2 centered at the origin. Thus we get the following integral and change to polar
coordinates to evaluate:
2π 2 θ =0 r =1 (1 + x2 + y 2 )dA = (a)
R 2π (b) =
0 12 14
r+ r
2
4 2 2π dθ =
1 0 2π 2 θ =0 (1 + r 2 )r dr dθ = r =1 r + r 3 dr dθ 21
21
21π
dθ = 2π ·
=
4
4
2 y
z
R
1 2 x z = 1 + x2 + y 2
R x y 5. We need the projection R, of the object into the yz plane. So we need the projection of the
intersection of y = 2x and x + z = 1 in the yz pl...
View
Full
Document
This note was uploaded on 01/20/2014 for the course MATH 13 taught by Professor Weiss during the Spring '07 term at Tufts.
 Spring '07
 Weiss
 Math, Calculus

Click to edit the document details