5.2 The Definite Integral 

[STARTS AT 7:10]

LECTURER: Use the formula for area of a circle to evaluate the integral from 3 to 6 of the square root of 9 minus x minus 3 squared. All right, so this equation actually is an upper half circle going from 0 to 6 is this endpoint. And the middle point of that is 3. 

So here is the area I am seeking to find. The area from 3 to 6 of that function right there. Now if you notice, this is a semicircle with a radius of 3. Actually what we want is the quarter circle. So the integral of square root of 9 minus x minus 3 squared equals 1/4 pi r squared. In this case our r is 3. So this is 9/4 pi, which is roughly 7.069. 

So that would be the area. So it pays, certainly, to be able to recognize functions and what the graphs are going to look like from them.

[ENDS AT 8:39]