volume using cross-sections

label Calculus
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May 17th, 2015

after you have graphed the function the three "functions" y=x, y=4, x=0.
notice you are revolving an infinitisimal vertical strip above y=x and below y=4
the figure would be a cylinder that has taken a cone from it.

for the strip

dV= pi(R2^2-R1^2)dx
R2=4
R1=x
thus
dV =pi(16-x^2)dx
integrate
V=pi(16x -x^3/3) from 0 to a
solving for a
y=4, y=x
thus x=4
then a=4
V=pi(16x -x^3/3) from 0 to 4
V=((pi(16*4 -(4)^3/3)-0)
V=128/3pi u^3 ;-)      


May 17th, 2015

where you got the y=4 from?

May 17th, 2015

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May 17th, 2015
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May 17th, 2015
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