Ch 5.2 Graphical, Numerical, Algebraic by Finney Demana, Waits, Kennedy

1. Ch 5.2Graphical, Numerical, Algebraic by Finney Demana, Waits, Kennedy

4. Reimann Sums During the last class, we’ve looked at approximating the total distance traveled between times a and b, by summing up rectangles and either getting an overestimation or an underestimation. LRAM RRAM These approximations gotten from summing up a number of rectangles, are called Reimann sums.

5. Sigma Notation The more rectangles you have within the same interval, the more accurate your approximation becomes. You have complete precision if you take the limit of these sums as the number of rectangles you use approaches infinity.

7. Definite Integral Given that f(t) is non-negative, continuous for a ≤ t ≤ b. The definite integral of from a to b is written:

8. Example

9. Example Notice that in this graph that both the width Δx and the height f(x) are positive which gives us positive area. What happens if f(x) is negative?

10. Example

11. Example

12. Discontinuous Functions Some functions with discontinuities are also integrable. A bounded function that has a finite number of points of discontinuity on an interval [a, b] will still be integrable on the interval if it is continuous everywhere else.

13. Discontinuous Function Try this on your calculator using fnInt…