End of Mardi Gras Reflection

Ok so i needed something old to review for this weeks blog an I didn't wanna repeat somethin so here's one I never did: Disks an Washers!

There are 2 formulas you have to know:

Disk Formula: ( pi )S( r^2 )dx
Washer Formula: ( pi )S( top^2 )-( bottom^2 )


EXAMPLE: Find the volume of the solid formed by revolving the region bounded by the
graphs of y = (square root of (x)) and y = x^2 about the x-axis.
First, you plug in the 2 equations into your calculator and graph them.


For this graph, its a washer, an we know that from graphin it in our calculadoras.
-To find the bounds, set the 2 eqns = to each other
(square root of (x))^2 = (x^2)^2
x = x^4
x^4 - x = 0
x(x^3 -1) = 0
x = 0, 1
Plug into the formula.
(pi)1/S/0 (square root of (x))^2 - (x^2)^2
(pi)1/S/0 x - x^4
Find the integral.
pi[1/2x^2 - 1/5x^5]
Plug in the bounds.
(pi)[1/2(1)^2 - 1/5(1)^2] - [1/2(0)^2 - 1/5(0)^2]
= 3pi/10