This document discusses numerical integration. It defines integral calculus as dealing with functions to be integrated, and notes that integration is the reverse of differentiation. It describes the integral symbol and states that integration can be definite or indefinite. It lists several uses of integration, such as finding the area under a curve or the volume of a solid. The document does not provide clear summaries.

1. NUMERICAL
Owe n A.
Ran a , Ia n
INTEGRATION

2. NUMERICAL INTEGRATION
Integral Calculus - is the branch of
calculus which deals with functions to be
integrated.
Integration is the reverse process of
differentiation. The function to be
integrated is referred to as integrand
while the result of an integration is called
integral.

3. NUMERICAL INTEGRATION
The Integral symbol is an elongated S - denoting
sum, was introduced by Leibniz, who named
integral calculus as calculus summatorious.
TYPES
1. Definite Integral – defined by the limit values a &
b of the independent variable.
2. Indefinite/Primitive Integral – an integral with no
restrictions imposed on its independent
variable.

4. NUMERICAL INTEGRATION
DEFINITE INTEGRAL INDEFINITE INTEGRAL

5. NUMERICAL INTEGRATION
USES:
1. How to find the Area
2. How to locate the Centroid
3. How to find the Arc Length of a Graph
4. How to find the Surface Area of a Solid
5. How to find the Volume of a Solid Figure
6. How to Solve for the Work Done
7. How to Solve the Moment of Inertia

6. NUMERICAL INTEGRATION

7. NUMERICAL INTEGRATION

8. NUMERICAL INTEGRATION

9. NUMERICAL INTEGRATION

10. NUMERICAL INTEGRATION

11. NUMERICAL INTEGRATION
● Describe customer needs and wishes
● Explain the requirements

12. NUMERICAL INTEGRATION
● Describe the main attributes of the product
● Link the product attributes to customer
needs

13. NUMERICAL INTEGRATION

14. NUMERICAL INTEGRATION
● Summarize the special features and
advantages of the product being introduced

15. NUMERICAL INTEGRATION
● Explain the steps that now need to be taken

16. NUMERICAL INTEGRATION

17. NUMERICAL INTEGRATION

18. NUMERICAL INTEGRATION

19. NUMERICAL INTEGRATION

20. NUMERICAL INTEGRATION

21. NUMERICAL INTEGRATION

22. NUMERICAL INTEGRATION

23. NUMERICAL INTEGRATION

24. NUMERICAL INTEGRATION

25. NUMERICAL INTEGRATION

26. NUMERICAL INTEGRATION

27. NUMERICAL INTEGRATION

28. Nmer meth is not an elegant
u ical ods
subject. It is a lot oftech detailand
nical
dir w k. Bu itisth w w sol mostofth r
ty or t e ay e ve e eal
w l pr l
ord obems.
h w .pu l
ttp://w w bic.asu.edu h u
/~ hang38/M E .h
A 384 tml

29. Thank You!!! :)

30. Questions??? :)