CBC-Chp-7-8-Nts - CalcBc Chp 7-8 Improper Integrals Notes...

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Chp 7-8 Improper Integrals Notes 1. There are two types of IMPROPER INTEGRALS to consider: (1) When the interval [a, b] involves (2) When the function f(x) is discontinuous within the interval [a, b] 2. INTEGRALS WITH INTERVALS INVOLVING Ex(consider area under a curve) Look at the area of f(x) = on the interval [1, t] where t A = dx = (apply the F.T.C.) = + 1 What is the area when t = 2 ? t = 3 ? t = 5 ? t = 10 ? A = 1/2 A = 2/3 A = 4/5 A = 9/10 What about when t ? The area, surprisingly (maybe not?) , is not a value near . The integral is improper if it is set up as dx . The interval [a, b] has to be endpoints with specific number values. Since t is not a specific number, LIMITS are used with integrals. dx = = 0 + 1 = 1 area under the curve maximum area approached 3. THREE CASES WHERE INTERVALS CAN INVOLVE (1) f(x) dx = = (2) f(x) dx = = (3) f(x) dx = f(x) dx + f(x) dx where c is your choice + + f(x) x
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CBC-Chp-7-8-Nts - CalcBc Chp 7-8 Improper Integrals Notes...

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