Questions from General Calculus

Q: The figure shows the region of integration for the integral ∫_0

The figure shows the region of integration for the integral ∫_0^1 ∫_(√x)^1 ∫_0^(1-y) f (x,y,z) dz dy dx Rewrite this integral...

Q: Use spherical coordinates. Find the mass and center of mass

Use spherical coordinates. Find the mass and center of mass of a solid hemisphere of radius a if the density at any point is proportional to its distance from the base.

Q: Use cylindrical or spherical coordinates, whichever seems more appropriate.

Use cylindrical or spherical coordinates, whichever seems more appropriate. Find the volume and centroid of the solid E that lies above the cone z = √(x^2+y^2 ) and below the sphere x2 + y2 + z+ = 1....

Q: Calculate the iterated integral ∫_0^(π/6)

Calculate the iterated integral ∫_0^(π/6) ∫_0^(π/2) (sin x+sin y ) dy dx

Q: Find the volume of the solid by subtracting two volumes.

Find the volume of the solid by subtracting two volumes. The solid under the plane z = 3, above the plane z = y, and between the parabolic cylinders y = x2 and y = 1 - x2

Q: Let D be the disk with center the origin and radius a

Let D be the disk with center the origin and radius a. What is the average distance from points in D to the origin?

Q: Use cylindrical or spherical coordinates, whichever seems more appropriate.

Use cylindrical or spherical coordinates, whichever seems more appropriate. Evaluate ∭E z dV, where E lies above the paraboloid z = x2 + y2 and below the plane z = 2y. Use either the Table of Integral...

Q: Use cylindrical or spherical coordinates, whichever seems more appropriate.

Use cylindrical or spherical coordinates, whichever seems more appropriate. (a). Find the volume enclosed by the torus ρ = sin φ. (b). Use a computer to draw the torus.

Q: Evaluate the integral by changing to spherical coordinates ∫_(-a)^

Evaluate the integral by changing to spherical coordinates ∫_(-a)^a ∫_(-√(a^2-y^2 ))^(√(a^2-y^2 ) ∫_(-√(a^2-x^2-y^2 ))^(√(a^2-x^2-y^2 ) (x^2 z+y^2 z+z^3) dz dx dy

Q: Evaluate the integral by changing to spherical coordinates ∫_(-2)^

Evaluate the integral by changing to spherical coordinates ∫_(-2)^2 ∫_(-√(4-y^2))^(√(4-y^2)) ∫_(2-√(4-x^2-y^2))^(2+√(a^2-x^2-y^2) (x^2+y^2+z^2) ^(3/2) dz dy dx