MATH 241 Quiz: MATH 241 UPenn Solution to Quiz 5

1. Let F(x, y, z)-. (a) Argue that F is conservative. (b) Find a function f such that F-v/. (c) Find φ (ze* + 1) dr + cos y dy + ez dz where S1 is the unit circle in the zy-plane. Si (d) Find F-dr where C is parametrized by r(t) =, 0 t T.

9) Evaluate Jc ez dz , where C is the line segment joining z1=0 toz2=2+ (Answer: e2 1-1)

I. Compute ▽f . dr where C is the line segment from (0,-12) to (1,3,0) and f(x,y, z) = ze* + xu"-22