Questions from General Calculus

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

Evaluate the triple integral. ∭E y dV, where E = {(x, y, z) | 0 < x < 3, 0 < y < x, x - y < z < x + y}

Q: Plot the point whose spherical coordinates are given. Then find the

Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point. (a). (6, π/3, π /6) (b). (3, π /2, 3 π/4)

Q: Evaluate the triple integral. ∭E ez/y dV

Evaluate the triple integral. ∭E ez/y dV, where E = {(x, y, z) | 0 < y < 1, y < x < 1, 0 < z < xy}

Q: (a). Show that when Laplace’s equation (∂^2 u)/(∂

(a). Show that when Laplace’s equation (∂^2 u)/(∂x^2 ) + (∂^2 u)/(∂y^2 ) + (∂^2 u)/(â&...

Q: Sketch the solid whose volume is given by the integral and evaluate

Sketch the solid whose volume is given by the integral and evaluate the integral. ∫_0^(π/6) ∫_0^(π/2) ∫_0^3 ρ^2 sin φ dρ dθ dφ

Q: Sketch the solid whose volume is given by the integral and evaluate

Sketch the solid whose volume is given by the integral and evaluate the integral. ∫_0^(π/4) ∫_0^2π ∫_0^secφρ^2 sin φ dρ dθ dφ

Q: Set up the triple integral of an arbitrary continuous function f (

Set up the triple integral of an arbitrary continuous function f (x, y, z) in cylindrical or spherical coordinates over the solid shown.

Q: Plot the point whose spherical coordinates are given. Then find the

Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point. (a). (2, π/2, π/2) (b). (4, -π/4, π/3)

Q: Set up the triple integral of an arbitrary continuous function f (

Set up the triple integral of an arbitrary continuous function f (x, y, z) in cylindrical or spherical coordinates over the solid shown.

Q: Use spherical coordinates. Evaluate ∭E xe^(x^

Use spherical coordinates. Evaluate ∭E xe^(x^2+y^2+z^2 ) dV, where E is the portion of the unit ball x2 + y2 + z2 < 1 that lies in the first octant