1. Introduction to the Definite Integral Unit 6 Lesson 2 E. Alexander Burt Potomac School

3. The area under the curve is approximately the sum of the area of those rectangles

4. The more rectangles we sum (and the smaller D x gets) the closer our approximation will get to the actual area.

5. Riemann Sums A larger number of sub-intervals results in a closer approximation. Note that all the approximations approach a specific value. http://commons.wikimedia.org/wiki/File:Riemann_sum_convergence.png

7. Calculus Lawyer Talk: if the function is continuous from a to b, the definite integral over the interval a to b exists.

11. The function is fnInt and it is in the Math menu

12. The syntax is fnInt(f(x), x, a, b)

13. Example: try the integral of x 2 from 0 to 4

14. FnInt (x^2, x, 0, 4) = 21.33333

16. See that it approaches the correct value: 21.333 as we found out earlier. Subintervals Approximate Sum 4 14 8 17.5 16 19.375 128 21.08

18. The integral of a linear function is a triangle

19. The integral of a semicircle is A=1/2 p r 2

20. Adding a constant to a function adds a rectangle to the integral: the integral of f(x)+k = the integral of f(x) + k(b-a)