# volume of solid

• Mar 4th 2009, 04:31 PM
alex83
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
• Mar 4th 2009, 06:08 PM
skeeter
Quote:

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 ...

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

washers ...

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

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

$\displaystyle 1 - tan^2{y} = 1 - (sec^2{y} - 1) = 2 - sec^2{y}$
• Mar 4th 2009, 06:14 PM
alex83
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
• Mar 5th 2009, 04:46 AM
skeeter
Quote:

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.
• Mar 5th 2009, 05:40 AM
galactus