ap calculus slides february 8, 2008

12
Focault-pendel More about volumes of revolution ...

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More on solids of revolution.

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Page 1: AP Calculus Slides February 8, 2008

Focault-pendel

More about volumes of revolution ...

Page 2: AP Calculus Slides February 8, 2008
Page 3: AP Calculus Slides February 8, 2008
Page 4: AP Calculus Slides February 8, 2008
Page 5: AP Calculus Slides February 8, 2008
Page 6: AP Calculus Slides February 8, 2008
Page 7: AP Calculus Slides February 8, 2008

Any function rotated about the x-axis will have circular cross sections and it's volume can be found by:

In General:

A(x) is the function representing the changing areas

... so you need a function that represents r.

With circular cross sections

Page 8: AP Calculus Slides February 8, 2008
Page 9: AP Calculus Slides February 8, 2008

Let's look at another function ...

Page 10: AP Calculus Slides February 8, 2008
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Page 12: AP Calculus Slides February 8, 2008