Questions from General Calculus

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

Use spherical coordinates. Evaluate ∭E √(x^2+y^2+z^2 ) dV, where E lies above the cone z = √(x^2+y^2 ) and between the spheres x2 + y2 + z2 − 1 and x2 + y2 + z2 = 4.

Q: Use spherical coordinates. Find the average distance from a point

Use spherical coordinates. Find the average distance from a point in a ball of radius a to its center.

Q: Change from rectangular to spherical coordinates. (a). (

Change from rectangular to spherical coordinates. (a). (0, -2, 0) (b). (-1, 1, - 2 )

Q: Change from rectangular to spherical coordinates. (a). (

Change from rectangular to spherical coordinates. (a). (1, 0, 3 ) (b). ( 3 , -1, - 3 )

Q: If f is continuous, show that ∫_0^x ∫_

If f is continuous, show that ∫_0^x ∫_0^y ∫_0^z f(t) dt dz dy =1/2 ∫_0^x (x-t)^2 f(t)dt

Q: Evaluate the iterated integral. ∫_1^2 ∫_0

Evaluate the iterated integral. ∫_1^2 ∫_0^2x ∫_0^lnxxe^(-y) dy dx dz

Q: Evaluate the iterated integral. ∫_0^1 ∫_0

Evaluate the iterated integral. ∫_0^1 ∫_0^1 ∫_0^(√(1-z^2 ))z/(y+1) dx dz dy

Q: The figure shows the solid enclosed by three circular cylinders with the

The figure shows the solid enclosed by three circular cylinders with the same diameter that intersect at right angles. In this project we compute its volume and determine how its shape changes if the...

Q: In this project we find formulas for the volume enclosed by a

In this project we find formulas for the volume enclosed by a hypersphere in n-dimensional space. 1. Use a double integral and trigonometric substitution, together with Formula 64 in the Table of Inte...

Q: Suppose that a solid ball (a marble), a hollow ball

Suppose that a solid ball (a marble), a hollow ball (a squash ball), a solid cylinder (a steel bar), and a hollow cylinder (a lead pipe) roll down a slope. Which of these objects reaches the bottom fi...