Problem 1

Find the mass of the rectangular region , with density function .

Problem 2

A lamina occupies the part of the rectangle , and the density at each point is given by the function .

(a). What is the Total Mass?

(b). Where is the Centre of Mass

Problem 3

A lamina occupies the part of the disk in the first quadrant and the density at each point is given by the function

(a). What is the Total Mass

(b). Where is the Centre of Mass

Problem 4

Find the triple integral of the function over the cube , , and .

Problem 5

Evaluate where is the box determined by , , and .

Problem 6

Evaluate the triple integral where is the solid , , and .

Problem 7

Set up a triple integral to find the mass of the solid tetrahedron bounded by the xy-plane, the yz-plane, the xz-plane, and the plane , if the density function is given by . Write an iterated integral of the form .

Problem 8

Find the volume enclosed by the paraboloids and .