2 The Definite Integral The definite integral as the area of a region If f is continuous and non-negative on the closed interval a b then the area of the region bounded by the graph of f the x-axis and the vertical lines x a and x b is given by Area This is called the definite integral. 3 The Definite Integral
where ci is any point in the ith interval and At this point we evaluate a definite integral using area formulas of common geometric regions if possible. (In the next section we will calculate the definite integral using other methods) 4 Using Common Geometric Figures Example 5 Using Common Geometric Figures Example 6 Using Common Geometric Figures Example 7 Using Common Geometric Figures Example 8 Properties of the Definite Integral 9 Definite Integrals area above area below 10 Properties 11 Example If and then find 12 Example Set up a definite integral that yields the area of the region. 13 Example Set up a definite integral that yields the area of the region. 14 Homework
Section 4.3 page 278 13 19 odd 23 43 odd
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