1)Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = 8x³, y = 0, x = 1; about x = 2.

2)Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

xy = 5, x = 0, y = 5, y = 7

3)Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.

x = 4 + (y 5)², x = 13

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about x = 3.

y = 5x⁴, y = 0, x = 2

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.

y = 9x x², y = 18; about x = 3

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8.

8y = x³, y = 0, x = 4

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.

y = x² + 23x 132, y = 0; about the yaxis

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.

y² x² = 4, y = 3; about the x-axis

The region bounded by the given curve is rotated about the specified axis. Find the volume V of the resulting solid by any method.

x² + (y 4)² = 16; about the y-axis

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.

x = (y 4)², x = 1; about y = 3

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.

y = 32 x², y = x²; about x = 4