1. The Net Change
The net change =

2. The Net Change
The net change =

3. 1 2 1 MATH-101 MATH-102 MEAN VALUE THEOREM FOR DEFINITE INTEGRALS
there is at least one number c in (a, b) 1
f(x) is continuous on [a, b] 2
f(x) is differentiable on (a, b)
MATH-102
MEAN VALUE THEOREM FOR DEFINITE INTEGRALS
at some point c in (a, b) 1
f(x) is continuous on [a, b]

4. 1 MEAN VALUE THEOREM FOR DEFINITE INTEGRALS
at some point c in (a, b) 1
f(x) is continuous on [a, b]

5. The Definite Integral
EXAM-1
TERM-102

6. THE DEFINITE INTEGRAL
Term-092

7. THE DEFINITE INTEGRAL
Term-092

8. THE DEFINITE INTEGRAL
Term-082

9. Term-092

10. THE DEFINITE INTEGRAL
Term-103

11. DEFINITION

12. TERM-091

13. TERM-082

14. TERM-082

15. INDEFINITE INTEGRALS
TERM-092

16. INDEFINITE INTEGRALS

17. THE SUBSTITUTION RULE
T-102

18. THE SUBSTITUTION RULE
092

19. THE SUBSTITUTION RULE
082

20. THE SUBSTITUTION RULE
092

21. THE SUBSTITUTION RULE
Find
Find

22. Even and Odd
Term-102

23. Even and Odd
Term-102

24. Even and Odd

25. Types of Discontinuities.
Continuity
Types of Discontinuities.
removable
discontinuity
infinite
discontinuity
jump
discontinuity

26. Integrabel Function
Differentiable
integrable
Continuous

27. Integrabel Function integrable Continuous integrable
number of removable and jump discontinuities are finite

28. Integrabel Function integrable
number of removable and jump discontinuities are finite
integrable

29. Integrabel Function
number of removable and jump discontinuities are finite
integrable
For integrability to fail, a function needs to be sufficiently discontinuous that the region between its graph and the x-axis cannot be approximated well by increasingly thin rectangles.
EXAMPLE: