I have exams coming up, and need some help with some homework problems that I'm really having difficulties with. I would appreciate either a step by step or something to get me on my way. Thanks!
2. 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???
4. Find the area bounded by the curves f(x)=x^3+x^2 and g(x)= 2x^2+2x
5. A cylindrical hole is drilled through the center of a sphere of radius R. Use the method of cylindrical shells to find the volume of the remaining solid, given that the solid is 6 cm high.
24. Find the volume of the solid generated by revolving about the line x=-1, the region bounded by the curves y= -x^2 + 4x -3 and y=0.
25. Consider the region in the xy-plane between x=0 and x=pi/2, bounded by y=0 and y=sin(x). Find the volume of the solid generated by revolving this region about the x-axis.
30. Let R be the region bounded by y=(1/x), y=x^2, x=0, and y=2. Suppose R is revolved about the x-axis. Set up but do not evaluate the integrals for the volume of rotation using (a) the method of cylindrical shells; (b) the method of circular disks.