Questions from General Calculus

Q: Evaluate the triple integral. ∭E 6xy dV, where

Evaluate the triple integral. ∭E 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by the curves y = √(x ), y = 0, and x = 1

Q: Evaluate the triple integral. ∭E (x – y

Evaluate the triple integral. ∭E (x – y) dV, where E is enclosed by the surfaces z = x2 - 1, z = 1 - x2, y = 0, and y = 2

Q: Use Lagrange multipliers to give an alternate solution to the indicated exercise

Use Lagrange multipliers to give an alternate solution to the indicated exercise in Section 14.7. Exercise 43. 14.7 Exercise 43: Find the points on the cone z2 = x2 + y2 that are closest to the poin...

Q: Evaluate the triple integral. ∭T y2 dV, where

Evaluate the triple integral. ∭T y2 dV, where T is the solid tetrahedron with vertices (0, 0, 0), (2, 0, 0), (0, 2, 0), and (0, 0, 2)

Q: Use the given transformation to evaluate the integral. ∬R

Use the given transformation to evaluate the integral. ∬R x2 dA, where R is the region bounded by the ellipse 9x2 + 4y2 = 36; x = 2u, y = 3v

Q: Use the given transformation to evaluate the integral. ∬R

Use the given transformation to evaluate the integral. ∬R (x2 - xy + y2) dA, where R is the region bounded by the ellipse x2 - xy + y2 = 2;

Q: Use the given transformation to evaluate the integral. ∬R

Use the given transformation to evaluate the integral. ∬R xy dA, where R is the region in the first quadrant bounded by the lines y = x and y = 3x and the hyperbolas xy = 1, xy = 3; x = u/v, y = v

Q: Use the given transformation to evaluate the integral. ∬R

Use the given transformation to evaluate the integral. ∬R y2 dA, where R is the region bounded by the curves xy = 1, xy = 2, xy2 = 1, xy2 = 2; u = xy, v = xy2. Illustrate by using a graphing calculato...

Q: Use spherical coordinates. Evaluate ∬B (x2 + y2

Use spherical coordinates. Evaluate ∬B (x2 + y2 + z2)2 dV, where B is the ball with center the origin and radius 5.

Q: Use spherical coordinates. Evaluate ∭E (x2 + y2

Use spherical coordinates. Evaluate ∭E (x2 + y2) dV, where E lies between the spheres x2 + y2 + z2 = 4 and x2 + y2 + z2 = 9.