Could someone please help me with the following area and volume problems?
-Find the volume of the solid formed when the region bounded by the curves y=x^3 +1, x=1, and y=0 is rotated about the x-axis. How do I do something like this for a volume of the solid problem with three curves???
-Find the area bounded by the curves f(x)=x^3 +x^2 and g(x)=2x^2 +2x.
What the problem states, is that you need to find the solid rotation between y=x^3 +1, x=1, and the x-axis y=0.
How y=0 does help you? You don't even need to draw the graphic.
Just find x^3+1=0, that is the intersection between the x-axis and y=x^3+1.
In problems like these usually you need to find intersection points, and it is often very useful to draw the graphics of the functions.
So you need to find the solid rotation of x^3+1 from -1 to 1. Integrals will help you do that.
@undefined you do not need boundaries. The graphs of the functions are intersecting. Just find the intersecting points.