Homework # 22 - Math 250
The problems on this homework must be done alone. The honor code is in effect.
First name: Last name:
1. Say C1:→r1(t),a≤t≤b, and C2:→r2(t),c≤t≤d are two piecewise smooth curves such that →r2(c)=→r1(a), and →r2(d)=→r1(b). Is it true that ∫C2→F⋅d→r=∫C2→F⋅d→r?
a. Definitely yes.
b. Definitely no.
a. It could possibly happen.
2. Say C1:→r1(t),a≤t≤b, and C2:→r2(t),c≤t≤d are two piecewise smooth curves such that →r2(c)=→r1(a), and →r2(d)=→r1(b), and →F is conservative. Is it true that ∫C2→F⋅d→r=∫C2→F⋅d→r?
3. Evaluate ∫C⟨x+y,x−y⟩⋅d→r, where C is the path that starts at (0,0), goes in a straight line to (1,1), then goes in a straight line to (3,-1), then goes in a straight line to (5, 1), and then goes in a straight line to (6,0). (Hint: if you're working hard on this one, you're working too hard.)
a. 12
b. 16
a. 18
b. 24
b. 30