Hello back again for another scribe, Tuesday's class was not very difficult although very important. As we began the day with a simple question, which was "Find the volume generated between the x-axis and the graph f(x)=x^2, from x=0 to x=2. Here is the graph of x^2.

http://fooplot.com/x^2

So we begin to solve this problem by setting up the equation (0,2) ∫ πr^2 dx

= (0,2) ∫ Π(x^2)^2 dx

= (0,2) ∫ Πx^4 dx

= (0,2) ∫ Π(x^5/5) dx

= Π(2^5/5) - Π(0^5/5)

= 32Π/5

Solved.

Then Mr.K began showing us a new form in which solids of revolution can be formed, which was by rotating the function about the y-axis. The equation that represents a function about the y-axis is: V= ∫2 Πrf(x) dx Here is a problem that was worked on in class using this method.

Region S is bonded between two functions, f(x) & g(x), find the volume of the solid generating around the y-axis.

F(x)= 0.5x^2-2x+4 G(x)= 4+4x-x^2

Using the volume equation of a solid of revolution around the y-axis we get, just solve algebraically, do not solve completely:

= 2 Π (0,4)∫ x [g(x)-f(x)] dx

All in all this class was very important as the equation for a solid of revolution about the y-axis was given and explained. Remember all the rest of 8.3 was for homework. The next scribe is VAN.

## Wednesday, February 13, 2008

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