Calculus III

1. Find the curl of the vector field given by F(x, y, z) = ex sin y i – ex cos y j.

2. Find the divergence of the vector field F(x, y) = x2i + 2y2j.

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3. Find a potential function for the conservative vector field F(x, y) = 2xyi + (x2 – y)j.

4. Evaluate the line integral given below where C is the path r(t) = 4ti + 3tj, 0 ? t ? 1.

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5. Use the Fundamental Theorem of Line Integrals to evaluate the line integral

where C is the parabola y = 4 – x2 from (2, 0) to (0, 4).

xyds

C ?

xyds

C

ò

2xydx + ( x2

C ? + y2 )dy

2xydx+(x

2

C

ò

+y

2

)dy