Math 241 - Quiz #10

Covers 12.3 and 12.4

1. integrate xy over D, 0 <= x <= 1, x^2 <= y <= sqrt(x)

2. integrate xy over R, 1st quadrant, between x^2+y^2=4 and x^2+y^2=25

Solution

1. I from 0 to 1, I from x^2 to sqrt(x) xy dy dx
= I from 0 to 1 x^2/2 - x^5/5 dx
= 1/12

2. I from 0 to pi/2, I from 2 to 5 r^3 cos(th) sin(th) dr dth
= I from 0 to pi/2 609/4 cos(th) sin(th) dth
= 609/8

ccollins@math.utk.edu
Last Modified: Mar. 29, 1999