The Disk Method Worksheet with Answer Key

What's on the worksheet

1. Each region lies under the given curve and above the x-axis on the given interval.
   y = \dfrac{x^2}{2}, \ 0 \le x \le 2y = \dfrac{3}{x}, \ 1 \le x \le 3y = \dfrac{1}{\sqrt{1 + x^2}}, \ 0 \le x \le 1
2. The region in the first quadrant bounded by the curve y = 1x², the y-axis and the lines y = 1 and y = 4 is revolved about the y-axis.
3. The line y = 4 touches the parabola y = 4x - x² at its vertex.
4. y = \ln x x = e x y The region bounded by y = x, the x-axis and the line x = e, shown in the figure, is revolved about the line x = e.
5. Luis throws a vase on a potter's wheel, so its inside is a solid of revolution about the vase's vertical center line.
6. Let r > 0 and h > 0.