Math 241 - Quiz #14

1. 13.3 # 13
2. 13.4 # 11

Solution

1. F is conservative and F = grad f, where f = x^2 y^3
so int_C F. dr = f(r(pi/2)) - f(r(0))
= f(1,pi^2/4+1) - f(0,1) = (pi^2/4+1)^3

2. By Green's Theorem: int_C xy dx + 2x^2 dy = int int_D 4x - x dA
Changing to polar coordinates we get
int_0^2 int_0^pi 3 r cos(theta) r dtheta dr
= int_0^2 r^2 sin(theta)|(pi,0) dr = 0.

ccollins@math.utk.edu
Last Modified: Apr. 26, 1999