Questions from General Calculus

Q: (a). Express the volume of the wedge in the first

(a). Express the volume of the wedge in the first octant that is cut from the cylinder y2 1 z2 − 1 by the planes y = x and x = 1 as a triple integral. (b). Use either the Table of Integrals (on Refere...

Q: (a). In the Midpoint Rule for triple integrals we use

(a). In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a triple integral over a box B, where f (x, y, z) is evaluated at the center (x ̅i, y ̅j, z ̅k) of the box Bij...

Q: Sketch the solid whose volume is given by the iterated integral.

Sketch the solid whose volume is given by the iterated integral. ∫_0^1 ∫_0^(1-x) ∫_0^(2-2z)〖dy dz dx〗

Q: Sketch the solid whose volume is given by the iterated integral.

Sketch the solid whose volume is given by the iterated integral. ∫_0^2 ∫_0^(2-y) ∫_0^(4-y^2) dx dz dy

Q: Evaluate the iterated integral. ∫_0^π ∫_0

Evaluate the iterated integral. ∫_0^π ∫_0^1 ∫_0^(√(1-z^2 )) z sin x dy dz dx

Q: Evaluate the integral in Example 1, integrating first with respect to

Evaluate the integral in Example 1, integrating first with respect to y, then z, and then x. Example 1:

Q: Evaluate the triple integral. ∭E z/(x^

Evaluate the triple integral. ∭E z/(x^2+y^2 ) dV, where E = {(x, y, z) | 1 < y < 4, y < z < 4, 0 < x < z j

Q: Evaluate the triple integral. ∭E sin y dV,

Evaluate the triple integral. ∭E sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0, 0), (π, 0, 0), and (0, π, 0)

Q: Use cylindrical coordinates. Evaluate ∭E √(x^2

Use cylindrical coordinates. Evaluate ∭E √(x^2+ y^2 ) dV, where E is the region that lies inside the cylinder x2 + y2 = 16 and between the planes z = -5 and z = 4.

Q: Use cylindrical coordinates. Evaluate ∭E z dV, where

Use cylindrical coordinates. Evaluate ∭E z dV, where E is enclosed by the paraboloid z = x2 + y2 and the plane z = 4.