How do you find the volume of the solid obtained by rotating the region bounded by the curves f(x)=3x^2f(x)=3x2 and g(x)=2x+1 g(x)=2x+1 about the x axis?

1 Answer
Gió
Jul 4, 2015

I found: 200pi/81200π81

Explanation:

First let us see the area that will be rotated:
enter image source here

the two graphs meet at x=1x=1 and x=-2/3x=−23 (values obtained solving the system formed by the two equations:
{y=3x^2{y=3x2
{y=2x+1{y=2x+1
We can use the "Cylinder" method to evaluate the volumes of the solid generated by the first function (line) and then subtract the volume of the second (parabola) as:
enter image source here

Related questions
See all questions in Determining the Volume of a Solid of Revolution
Impact of this question
6287 views around the world
You can reuse this answer
Creative Commons License