Questions from General Calculus

Q: Find the area of the surface. The part of the

Find the area of the surface. The part of the surface z = xy that lies within the cylinder x2 + y2 = 1

Q: (a). Use the Midpoint Rule for double integrals with m

(a). Use the Midpoint Rule for double integrals with m = n = 2 to estimate the area of the surface z = xy + x2 + y2, 0 < x < 2, 0 < y < 2. (b). Use a computer algebra system to approximate the surfac...

Q: Evaluate the triple integral. ∭E x dV, where

Evaluate the triple integral. ∭E x dV, where E is bounded by the paraboloid x = 4y2 + 4z2 and the plane x = 4

Q: Evaluate the triple integral. ∭E z dV, where

Evaluate the triple integral. ∭E z dV, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the first octant.

Q: Find, to four decimal places, the area of the part

Find, to four decimal places, the area of the part of the surface z = 1 + x2y2 that lies above the disk x2 + y2 < 1.

Q: Evaluate the integral ∭E (xy + z2) dV,

Evaluate the integral ∭E (xy + z2) dV, where E = {(x, y, z) | 0 < x < 2, 0 < y < 1, 0 < z < 36 using three different orders of integration.

Q: Find, to four decimal places, the area of the part

Find, to four decimal places, the area of the part of the surface z = (1 + x2) / (1 + y2) that lies above the square |x | + |y | < 1. Illustrate by graphing this part of the surface.

Q: Use a triple integral to find the volume of the given solid

Use a triple integral to find the volume of the given solid. The solid enclosed by the cylinder y = x2 and the planes z = 0 and y + z = 1

Q: Use a triple integral to find the volume of the given solid

Use a triple integral to find the volume of the given solid. The solid enclosed by the cylinder x2 + z2 = 4 and the planes y = -1 and y + z = 4

Q: Evaluate lim┬(n→∞)n^(-2) ∑_(i=

Evaluate lim┬(n→∞)n^(-2) ∑_(i=1)^n ∑_(j=1)^(n^2) 1/√(n^2+ni+j)