# Math 1501

Quiz #10

## November 11, 1999

Tom Morley

Name: ____________________________

*Don't Panic*

### Open Book and Notes. You have 30 minutes. Carefully explain your proceedures and answers

### Problem 1 (10 points)

A rod lies between x-0 and x = L. Its mass density is proportional to the cube of the distance from x = L Find the center of mass.

##### Calculations

### Problem 2 (10 Points)

Consider the region(s) bounded by y=0, y=4, and the ccurves y = and y = . Set up the area as a) Integral(s) with respect ot x, and b) Integral(s) with respect to y. Do not actually evaluate the integrals.

#### Calculations

##### a) As a y integral

You have to break the integral into two pieces, corresponding to the two pieces.

##### a) As an x integral

The first piece is not too bad --

The second piece has to be broken into two integrals...

### Problem 3 (10 Points)

Consider the region(s) bounded by y=0, y=4, and the ccurves y = and y = .Find the volume when this region is revolved arround the y axix. Hint Integrate with respect to y.

#### Answer