Calc
posted by Ashley on .
find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y=x^2+1; y=9x^2; about y=1

First find the intersections between the two curves, they are the limits of integration. They can be found readily as x=±2.
Next, we check that the curves do not cross the axis y=1 between the limits of integration. Otherwise the limits of integration must change.
Now use the washer method to calculate the area, since the "outer" radius R is based on the upper curve, and the inner radius r is on the lower curve.
The integration formula is then
Area = π∫(R(x)^2r(x)^2)dx