1/30/2011

Ok, this week went by extremelyyy too slow and I'm sure everyone else feels the same way, being that we had to come off of two 4-day weeks back to back. Anyway, this week in Calculus we did some UNO study packets, and to catch up with some of the other blogs I missed, we learned about finding the area and volume of two graphs.

To find the area between two curves,

f(x) and g(x)

You take the integral of (the top graph minus the bottom graph)

So, if g(x) is on "top", it would be

⌠g(x) - f(x)

Example:

f(x) = x^2 + 1

g(x) = -x^2 + 4

Find the area between these 2 graphs.

⌠(-x^2 + 4) - (x^2 + 1) dx

⌠ -2x^2 + 3 dx

x^2 + 1 = -x^2 + 4

2x^2 = 3

x^2 = 3/2

x = ± √3/2

-2/3 ((√3)/(2)) + 3((√3)/2) - [ -2/3 (-√3/2)^3 + 3(-√3/2))

= 4.899