1. 30. Section 5.2 The Definite Integral Table of Contents

2. The Definite Integral Essential Question – What does the notation for integrals look like and what does it mean?

3. Riemann Sums LRAM, MRAM, and RRAM are all Riemann Sums (after George Friedrich Bernard Riemann) In words – multiply all the values of the function (y values) with the width of the interval and add them all up

4. Definite Integrals A function must be continuous to take the integral Remember yesterday, we talked about if we take the limit as n approaches infinity of the sum, we will get the exact area If we take the limit of the Riemann Sum, we will get the definite integral

5. What the notation means Lower limit of integration Upper limit of integration Integrand Variable of Integration Integral symbol Read this as integral from a to b of f of x dx

6. Example Express as an integral

7. Area under a curve Area under a curve = Example Evaluate

8. Example Evaluate

9. Negative functions If f(x) is ever negative, you have to divide interval into subintervals where function is positive and where it is negative If f(x) is positive on [a,b] and negative on [b,c], Area under a curve =

10. Example Evaluate

11. Integral of a constant Example A train goes 75 mi/hr between 7 and 9 AM. How far does it go?

12. Other Integration Rules Order of Integration Zero Constant Multiple Sum and Difference

13. Rules cont…. Additivity Domination

14. Examples Given that Find

15. Assignment Pg. 321: #1-9 odd, 13, 17-25 odd, 50-62 all