# Thread: calc finding the volume

1. ## calc finding the volume

Use the shell method to find the volume of the solid of revolution obtained by rotating the region bounded by y = 1 and y = tan x about the x-axis from x = 0 to x = pi/4

2. Originally Posted by harry
Use the shell method to find the volume of the solid of revolution obtained by rotating the region bounded by y = 1 and y = tan x about the x-axis from x = 0 to x = pi/4

What have you tried...do you know where to start?

3. Originally Posted by harry
Use the shell method to find the volume of the solid of revolution obtained by rotating the region bounded by y = 1 and y = tan x about the x-axis from x = 0 to x = pi/4
Can someone check this please, i'm kind of rusty on the shell method.

so the shell method uses the formula:
V = int{2pi*x*h}dx where x is the radius and h is the height. since with this problem we are rotating about the x-axis, we will do our integral with respect to y.

y = tan(x)
=> x = arctan(y) ...........this is the height, see diagram

so
V = int{2pi*y*h}dy evaluated between 0 and 1
=> V = int{2pi*yarctan(y)}dy
=> V = 2pi*int{yarctan(y)}dy
=> V = 2pi [(y^2 + 1)/2 * arctan(y) - y/2] .......i used a formula forthis, but the integral can be done by parts i believe.

now we evaluate:
=> V = 2pi(arctan(1) - 1/2)
=> V = 2pi(pi/4 - 1/2)
=> V = (pi^2)/2 - pi
=> V = (pi^2 - 2pi)/2