1. Chapter 5 Integration Third big topic of calculus

2. Integration used to: Find area under a curve

3. Integration used to: Find area under a curve Find volume of surfaces of revolution

4. Integration used to: Find area under a curve Find volume of surfaces of revolution Find total distance traveled

5. Integration used to: Find area under a curve Find volume of surfaces of revolution Find total distance traveled Find total change Just to name a few

6. Area under a curve can be approximated without using calculus.

7. exact area. Then we’ll do it with calculus to find exact area.

8. Rectangular Approximation Method 5.1 Left Right Midpoint

9. 5.2 Definite Integrals

10. Anatomy of an integral integral sign

11. Anatomy of an integral integral sign [a,b] interval of integration a, b limits of integration

12. Anatomy of an integral integral sign [a,b] interval of integration a, b limits of integration a lower limit b upper limit

13. Anatomy of an integral integral sign [a,b] interval of integration a, b limits of integration a lower limit b upper limit f(x) integrand x variable of integration

14. Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 1. Zero Rule

15. Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 2. Reversing limits of integration Rule

16. Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 3. Constant Multiple Rule

17. Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 4. Sum, Difference Rule

18. Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 6. Domination Rule 6a. Special case

19. Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 7. Max-Min Rule

20. Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 8. Interval Addition Rule

21. Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 9. Interval Subtraction Rule

22. THE FUNDAMENTAL THEOREM OF CALCULUS PART 1 THEORY PART 11 INTEGRAL EVALUATION

23. INTEGRAL AS AREA FINDER Area above x-axis is positive. Area below x-axis is negative. “total” area is area above – area below “net” area is area above + area below

24. TEST 5.1-5.4 LRAM RRAM MRAM SUMMATION REIMANN SUMS RULES FOR INTEGRALS FUND. THM. CALC EVALUATE INTEGRALS FIND AREA TOTAL AREA NET AREA ETC……..