Calculus II, Spring 2016

Quiz 5

May 26, 2016

1. Rewrite ∫_{−1}^{1} ∫_{x^{2}}^{1} ∫_{0}^{1−y}dzdydx in the order dydzdx and dxdydz, respectively. Need not evaluate it.

2. Let D be the region bounded below by z = 0, above by x^{2} + y^{2} + z^{2} = 4 and the sides by x^{2} + y^{2} = 1. Express the volume of D in terms of dzdrdθ and dρdϕdθ, respectively. Need not evaluate it.

3. Evaluate ∫ ∫_{R} \sqrt{\frac{y}{x}} + \sqrt{xy}dxdy where R is the region bounded by xy = 1, xy = 4, y = x and y = 3x in the first quadrant.

4. Evaluate ∫_{C} \frac{x^{2}}{y^{\frac{4}{3}}} ds where x(t) = t^{2}, y(t) = t^{3}, 1 ≤ t ≤ 2

5. Evaluate ∫_{C} F · T ds where F = (x^{2}, −y) and C is the curve x = y^{2} from (4, 2) to (1, −1).