N=n => width = 1/n US = =1/n 3 [1+4+9+….+n 2 ] US =

1. . N=n => width = 1/n US = =1/n3[1+4+9+….+n2] US =

2. =

3. DefiniteIntegral We will define to be the limit as n approaches oo of where Dxi = (b-a)/n and is any point in the ith interval.

4. where Dxi = (b-a)/n and is any point in the ith interval, [xi-1,xi].

5. > 0 when f(x) > 0, but it is negative when f(x)<0. We will define to be the limit as n approaches oo of and is any point in the ith interval, [xi-1,xi].

6. DefinitionTheorems 1. 2. 3. 4.

7. DefinitionTheorems 5. 6. 7. 8.

9. If f(x) >= 0 on [a,b] then is the area under f(x) and over the x-axis between a and b.

10. If f(x) <= 0 on [a,b] then is the negative of the area over f(x) and under the x-axis between a and b.

11. [ • 0.50 • 0.1

12. [ • 2.0 • 0.1

13. ] • 0.0 • 0.1

14. [ • 1.0 • 0.1

16. [ • 1.5 • 0.1

17. 0

18. ] • 1.0 • 0.1

19. where Dxi = (b-a)/n and is any point in the ith interval, [xi-1,xi]. If the interval is [-4, 4] evaluate 8p

20. Pi = 3.14 • 6.28 • 0.1

21. Pi = 3.14 • -6.28 • 0.1