Rectangle volume using cross sections

[Myhappyending]

Homework Statement

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

Homework Equations

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?

 

[Villyer]

A=BH
A=B(1/2B)
A=3/2B

Calculus aside, the last statement is wrong.


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

 

[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.