geometric applications of the definite integral

1. 6. Find the volume of the solid generated by revolving the area bounded by xy = 1. x = 1, x = 4-, y = 0 about the x-axis. Find the volume of the solid generated by revolving about the y-axis the area bounded by);2 = 2.x+4andy2 =4 2x. Find the volume of the solid generated by revolving the area bounded by x2 + y2 = 4 about the line 2: = 2. (Use Washer Method) Find the volume of the solid generated by revolving about y = 4 the area bounded by y2 = 8x and y = 2:. (Use Washer Method) Find the volume of the solid generated by revolving about y = 4 the area bounded by y2 = 8x and y = 2:. (Use Cylindrical Shell Method) Find the volume of the solid generated by revolving the area bounded by y2 = 16 4x and x + y = 4 about the line 1: = 4. (Use Cylindrical Shell Method)