1 (5 points). Evaluate the line integral

if C2 is the path from (0,0) to (pi/2, 1) along the curve y = sin(x)

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2 (5 points).

a) Is the vector field

Exact? _____Yes______No

b) If your answer to a) is Yes, find a scalar field f such that F = --f. If your answer to a) is No, calculate the integral of F around the counterclockwise circle of radius 2, centered at the origin.

ANSWER: __________ = _________________________________________

c) Evaluate the closed loop integral

if C is the counterclockwise circle of radius 2, centered at the origin.

HINT: See if the answers to a) and b) help.

KEY FORMULA OR METHOD (optional for partial credit)____________________

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4 (5 points). Let R be the solid region inside both the sphere x² + y² + z² = 4 and the cone z = r(x² + y²). Let the density be f(x,y,z) = z. Set up an explicit integral for the total mass u and evaluate it:

The coordinates I am using are known as __________________coordinates.

The value of this integral is:

u = _____________________________

KEY FORMULA OR METHOD (optional for partial credit)____________________

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