I The region R is the region bounded by y = ln x, the x-axis, from x = 1 to x = e. (a)Set up the integral or integrals needed to find the area of R using partitions along the x-axis and then using partitions along the y-axis. (b)Using the method of disks or washers, set up the integral or integrals needed to find the volume when the region R is revolved about (i) the x axis (ii) the y-axis (iii) the line x = e. (c) Using the method of cylindrical shells, set up the integral or integrals needed to find the volume when the region R is revolved about (i) the x axis (ii) the y-axis (iii) the line x = e.
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I The region R is the region bounded by y = ln x, the x-axis, from x = 1 to x = e. (a)Set up the integral or integrals needed to find the area of R using partitions along the x-axis and then using partitions along the y-axis. (b)Using the method of disks or washers, set up the integral or integrals needed to find the volume when the region R is revolved about (i) the x axis (ii) the y-axis (iii) the line x = e. (c) Using the method of cylindrical shells, set up the integral or integrals needed to find the volume when the region R is revolved about (i) the x axis (ii) the y-axis (iii) the line x = e.
