# A few problems

• Jul 15th 2008, 03:41 PM
Zolthas
A few problems
I have a few problems on a review for a test on Thursday morning that I am either just not getting or I am not sure if I am right.

1) Find the arc length from (x1, y1) to (x2, y2) on the graph of f(x)=mx+b.

I just don't see how you can find the arc length of a straight line.

2) Find the volume formed by revolving the region bounded by the graphs of y=x^3+x+1, y=1, and x=1 about the line x=2 using the shell method.

3) Find the center of mass of the region bounded by the graphs of f(x)=4-x^2 and g(x)=x+2

4) A force of 750 pounds compresses a spring 3 inches from its natural length of 15 inches. Find the work done in compressing the spring an additional 3 inches.

For this one I got a force of 4500 in-lb for the entire 6 inches being compressed, and when I integrated from 3 to 6 I got 3375 in-lb for the additional 3 inches. I am not sure if this is right or not.

• Jul 15th 2008, 04:34 PM
Mathstud28
Quote:

Originally Posted by Zolthas
I have a few problems on a review for a test on Thursday morning that I am either just not getting or I am not sure if I am right.

1) Find the arc length from (x1, y1) to (x2, y2) on the graph of f(x)=mx+b.

I just don't see how you can find the arc length of a straight line.

2) Find the volume formed by revolving the region bounded by the graphs of y=x^3+x+1, y=1, and x=1 about the line x=2 using the shell method.

3) Find the center of mass of the region bounded by the graphs of f(x)=4-x^2 and g(x)=x+2

4) A force of 750 pounds compresses a spring 3 inches from its natural length of 15 inches. Find the work done in compressing the spring an additional 3 inches.

For this one I got a force of 4500 in-lb for the entire 6 inches being compressed, and when I integrated from 3 to 6 I got 3375 in-lb for the additional 3 inches. I am not sure if this is right or not.

$\displaystyle f(x)=mx+b$
$\displaystyle f'(x)=m$
$\displaystyle \sqrt{1+f'(x)^2}=\sqrt{1+m^2}$
$\displaystyle \int_{x_0}^{x_1}\sqrt{1+m^2}dx$
$\displaystyle =\sqrt{1+m^2}x\bigg|_{x_0}^{x_1}=\sqrt{1+m^2}\left (x_1-x_0\right)$