1. The problem statement, all variables and given/known data Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y=2x+15 and the parabola y=x2 about the following lines: a) The line x=5 b) The line x= -3 c) The x-axis d) The line y=25 Note: leave answer in terms of pi 2. Relevant equations v=2pi∫(shell radius)(shell height) 3. The attempt at a solution I know that I am making a mistake somewhere; I have a feeling that it is in my set... I am hoping that someone will be able to point it out to me. I am stuck on part a) and if I figure out my mistake I am confident that I will be able to do the other parts of the problem. First thing that I did (after graphing which is attached) was find the limits of integration: 2x+15=x2 x2-2x-15 (x-5)(x+3) So the limits of integration are from -3 to 5. v=2pi∫(5-x)(2x+15-x2)dx v=2pi∫10x+75-5x2-2x2-15x+x3 v=2pi∫75-7x2-5x+x3 v=2pi(75x-(7/3)x3-(5/2)x2+(1/4)x4 (plug in the limits of integration) v=2pi [(2125/12)+(607/4)] v=2pi(1973/6) v=1973pi/3 <---this answer is wrong. I hope that someone will be able to help me with this, thanks for stopping by and sorry for the crappy paint graph.