# Rectangle volume using cross sections

1. May 23, 2012

### Myhappyending

1. The problem statement, all variables and given/known data
Cross sections are perpendicular to the x axis and rectangle has the h=1/2b. The region is bounded by the area y=x^2, x axis and the line x=3

2. Relevant equations

3. The attempt at a solution
A=BH
A=B(1/2B)
A=3/2B
V=3/2(x^2-3)

just wondering if this is correct and how would i find where i integrate it to?

2. May 23, 2012

### Villyer

Calculus aside, the last statement is wrong.

And do your problems lie in finding the limits of integration?

3. May 23, 2012

### World

Ok so we will be integrating between x=0 and x=3. This is due to the region being bound by x=3 and y=x^2 (where y=0 @ x=0).

Therefore, V = (0∫3)* (x^2)(0.5(x^2)) dx

height (1/2b)-----------------^
base------------------^
-----------------^upper and lower limit of integration

A plain square would be calculated like this:

Therefore, V = (0∫3)* (x^2)(x^2) dx

*This is the format (lower limit∫upper limit)

Hope this helps, if you have a question let me know.

Last edited: May 23, 2012