volume of solid

**alex83** · March 4th 2009, 04:31 PM

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
about the y-axis

any help pls

**skeeter** · March 4th 2009, 06:08 PM

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
about the y-axis

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 ...

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

**alex83** · March 4th 2009, 06:14 PM

thanx for ur help

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

**skeeter** · March 5th 2009, 04:46 AM

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.

**galactus** · March 5th 2009, 05:40 AM

Also, see here:

http://www.mymathforum.com/viewtopic.php?f=15&t=6828

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