Questions from General Calculus

Q: Let R be the rectangle consisting of all points (x,

Let R be the rectangle consisting of all points (x, y) such that 0 ≤ x ≤ 2, 2 ≤ y ≤ 3. Calculate the following double integrals. Interpret each as a volume. ∫R∫ xy2 dx dy

Q: Let R be the rectangle consisting of all points (x,

Let R be the rectangle consisting of all points (x, y) such that 0 ≤ x ≤ 2, 2 ≤ y ≤ 3. Calculate the following double integrals. Interpret each as a volume. ∫R∫ (xy + y2) dx dy

Q: Let R be the rectangle consisting of all points (x,

Let R be the rectangle consisting of all points (x, y) such that 0 ≤ x ≤ 2, 2 ≤ y ≤ 3. Calculate the following double integrals. Interpret each as a volume. ∫R∫ e-x-y dx dy

Q: Let R be the rectangle consisting of all points (x,

Let R be the rectangle consisting of all points (x, y) such that 0 ≤ x ≤ 2, 2 ≤ y ≤ 3. Calculate the following double integrals. Interpret each as a volume. ∫R∫ ey-x dx dy

Q: Calculate the volumes over the following regions R bounded above by the

Calculate the volumes over the following regions R bounded above by the graph of f (x, y) = x2 + y2. R is the rectangle bounded by the lines x = 1, x = 3, y = 0, and y = 1.

Q: Draw the level curve of the function f (x, y

Draw the level curve of the function f (x, y) = xy containing the point (1/2, 4).

Q: Calculate the volumes over the following regions R bounded above by the

Calculate the volumes over the following regions R bounded above by the graph of f (x, y) = x2 + y2. R is the region bounded by the lines x = 0, x = 1 and the curves y = 0 and y = 3√x.

Q: Calculate the following iterated integrals. ∫01 (∫01 ex

Calculate the following iterated integrals. ∫01 (∫01 ex+y dy) dx

Q: Calculate the following iterated integrals. ∫-11 (∫-11 xy

Calculate the following iterated integrals. ∫-11 (∫-11 xy dx) dy

Q: Calculate the following iterated integrals. ∫-20 (∫-11 xexy

Calculate the following iterated integrals. ∫-20 (∫-11 xexy dy) dx