Integration by parts The Formula:
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Integration by partsThe Formula:
∫𝑢𝑑𝑣=𝑢 ∙𝑣−∫𝑣 𝑑𝑢Ultra Violet Voo Doo
The Idea: To express the original integral in terms of a second integral that you know how to integrate.
Use this formula for expressions that you don’t know how to integrate like
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I L A T E - What is u? dv? Inverse Trig Logarithmic Logarithmic (and Algebraic) Algebraic (and Exponential) Algebraic (and Trigonometric) Trigonometric (and exponential)
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Agenda: Feb. 6• 7.2 Integration by Parts – part deux• HW questions• An unusual solution – requires solving
the solution for the solution – huh?• Tabular method – a shortcut
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ILATE is a guideline, doesn’t always tell you what to pick for u. Choose that you know how to integrate. Trial and Error method.
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– a shortcut. Works well for problems with
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Homework
p. 494 #18, 19, 22, 36, 43, Tabular: 59-63 (odd) , 77, 99, 106
Not all will require IBP, some may be substitution!
1. Solve the initial value problem : ;
Continue working on Challenge problems
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Homework: