washer method calculus help The question is: "Find the volume of the solid obtained by rotating the region bounded by the line $y = 5$ using washer method outer - inner formula
 the functions to graph are: $y = x^2$, $y = 2x$. [sic, original reads, approximately, "Find the volume of the solid obtained by rotating the region bounded by $y = x^2$ and $y = 2x$ about $y = 5$."]
 A: To use the washer method, you calculate a difference of volumes by considering radial distances and using the formula $\pi r^{2}$. Thus, the problem comes down to finding appropriate expressions for $r$. 
You want to volume obtained by rotating the region between $y=x^{2}$ and $y=2x$ about the line $y=5$ so we do this stepwise:
1). Since you are rotating around a line parallel to the $x$-axis using the washer methhod, you will be integrating with respect to $x$, which runs from $0$ to $2$. 
2). . the distance from the line $y=5$ to the curve given by $y=x^{2}$ is $5-x^{2}$ so the volume we obtain by rotating the region between these curves is 
$$\pi \int_{0}^{2}(5-x^{2})^{2}dx$$
3). the distance from the line $y=5$ to the curve given by $y=2x$ is $5-2x$ so the volume we obtain by rotating the region between these curves is 
$$\pi \int_{0}^{2}(5-2x)^{2}dx$$
4). The volume we want is then the difference $$\pi \int_{0}^{2}(5-x^{2})^{2}dx-\pi \int_{0}^{2}(5-2x)^{2}dx=\frac{446}{15}\pi -\frac{62}{3}\pi \approx 28.5$$
