Raymond G.

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$ y = \sqrt{x - 1} $ , $ y = 0 $ , $ x = 5 $ ; about the x-axis

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$ y = e^x $ , $ y = 0 $ , $ x = -1 $ , $ x = 1 $ ; about the x-axis

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$ x = 2 \sqrt{y} $ , $ x = 0 $ , $ y = 9 $ ; about the y-axis

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$ 2x = y^2 $ , $ x = 0 $ , $ y = 4 $ ; about the y-axis

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$ y = x^3 $ , $ y = x $ , $ x \ge 0 $ ; about the x-axis

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$ y = 6 - x^2 $ , $ y = 2 $ ; about the x-axis