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Applications of Integration

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Applications of Integration

Volumes of Revolution

Many thanks to

http://mathdemos.gcsu.edu/shellmethod/gallery/gallery.html

Revolve this line around the x axis

2

5

We form a cylinder of volume

2

5

We can sum all the volumes to get the total volume

To find the volume of a cucumber…

we could slice the cucumber into discs and find the volume of each disc.

Volume of one slice =

We could model the cucumber with a mathematical curve and revolve this curve around the x axis…

25

-5

Each slice would have a thickness dx and height y.

r = y value

h = dx

Volume of one slice =

Area of 1 slice

Thickness of slice

and revolve it around the x axis

We can slice it up, find the volume of each disc and sum the discs to find the volume…..

Volume of one slice=

Radius = y

Area =

Thickness of slice = dx

y = 1

x = 0

y= 1

f(x)

g(x)

dx