1. The Definite Integral

7. In the previous section, we approximated area using rectangles with specific widths. If we could fit thousands of “partitions” ( rectangles with equal width ) whose width would approach zero into our curve, we would get a very good approximation of the area under this curve.

8. The Definite Integral In the previous section, we approximated area using rectangles with specific widths. If we could fit thousands of “partitions” ( rectangles with equal width ) whose width would approach zero into our curve, we would get a very good approximation of the area under this curve. Hence, we could use a summation notation to show this : - as the largest subinterval approaches a zero width

9. The Definite Integral In the previous section, we approximated area using rectangles with specific widths. If we could fit thousands of “partitions” ( rectangles with equal width ) whose width would approach zero into our curve, we would get a very good approximation of the area under this curve. Hence, we could use a summation notation to show this : We will simplify this into :

10. The Definite Integral EXAMPLE # 1 : Find

11. The Definite Integral EXAMPLE # 1 : Find

12. The Definite Integral EXAMPLE # 1 : Find

13. The Definite Integral EXAMPLE # 1 : Find

14. The Definite Integral EXAMPLE # 1 : Find

15. The Definite Integral EXAMPLE # 2 : Find

16. The Definite Integral EXAMPLE # 2 : Find

17. The Definite Integral EXAMPLE # 2 : Find

18. The Definite Integral EXAMPLE # 2 : Find

19. The Definite Integral

20. EXAMPLE # 3 : Evaluate

21. The Definite Integral EXAMPLE # 3 : Evaluate

22. The Definite Integral EXAMPLE # 3 : Evaluate

23. The Definite Integral EXAMPLE # 3 : Evaluate

24. The Definite Integral EXAMPLE # 3 : Evaluate

25. The Definite Integral EXAMPLE # 3 : Evaluate