Find the volumes of the solid formed when each of the areas in the following perform one revolution about the X axis...
Question: The volume line in the first quadrant and bounded by the curve y=x^3 and the line y=3x+2.
Volume of revolution about X-axis: V=pi*integral(y^2) dx. ('b' upper, and 'a' lower limit)
The Attempt at a Solution
Ok so I can find the volume (I think) of the whole system, but I can't just find the volume in the first quadrant.
V=pi*integral[(3x+2)^2 - (x^3)^2] between 2 and -1. So this is area under line minus area under curve, between there intersections. I don't know how to find the area in the first quadrant alone though!
I got V= 264pi/7 (the whole system) and the answer in my textbook is 56pi/5. Also sometimes the textbooks are wrong.