# Thread: volume of solid

1. ## volume of solid

et R be the region in the plane bounded by the x-axis and the line x=1 and the curve y= arc tan x
determine the volume of the solid obvtained by revolving R

any help pls

2. Originally Posted by alex83
et R be the region in the plane bounded by the x-axis and the line x=1 and the curve y= arc tan x
determine the volume of the solid obvtained by revolving R

any help pls
shells ...

$V = 2\pi \int_0^1 x \cdot \arctan(x) \, dx$

washers ...

$V = \pi \int_0^{\frac{\pi}{4}} 1 - \tan^2{y} \, dy$

washers looks like it may be easier to do ...

$1 - tan^2{y} = 1 - (sec^2{y} - 1) = 2 - sec^2{y}$

3. ## change the revolving axis

thanx for ur help

if i want to change the revolving axis to x=1 how does that effect the integral limits

4. Originally Posted by alex83
thanx for ur help

if i want to change the revolving axis to x=1 how does that effect the integral limits
doesn't affect the limits of integration ... it does affects the radius of revolution.