4. 1. Graph 2. Find the area between the above graph and the x-axis 3. 4. Find the area of each: 7

5. SWBAT: Find the exact area under a curve!

6. 1.Use midpoint Riemann sum with 4 equal subintervals of equal length to approximate the area under the velocity curve of a rocket’s flight. 2.Think about, then discuss what the units might be.

10.  In general, the sum of all rectangles is:  Where:  Let’s try an example! and

11. Before this is computed, we need some info:

12.  If not, review at the end

14.  Find the area under the curve of y=x 2 on the interval [0,3]

17.  The process of adding up an infinite number of rectangles with width dx is called...

19.  In the notation  f(x) is called the integrand  a is the lower limit  b is the upper limit

21.  Calculate

22.  Evaluateby interpreting it in terms of area.

24.  Therefore

25.  Similarly we can interpret as the difference of areas of two triangles:

28.  We can define using the following property:  If a = b, then ∆x = 0 and so

30.  Find your notes:

31.  Riemann sums with sigma  Definition of definite integral  Interpreting definite integrals as areas

32.  p.364 #5a,c, 8b  p.366 #33,35,37 56 days ‘til AP exam “When I take it, I will pass!