The first problem I have a problem with, the answer is 16pi/7 . The problem is:
1. "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".
My problem is I never really got the concepts of what to do where and when. I graph it 2 dimensionally, I get a shape sort of like a curved rhombus. I get to pick what method I use for this.
I think, using the disk method, x^3+1 would be the disk radius and the differential volume would be dv=pi*(x^3+1)^2 dx. Am I right so far? Here I get totally lost.
How would I use the shell method here?
2. "Find the surface area of a solid formed by rotating the region bounded by x^3/9, the X axis, and 0 <= x <= 2 about the X-axis" , the answer for this is 98pi/81. I'm missing the same concept from the first one.