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MAT 1221 Survey of Calculus Section 7.1 Integration by Parts http://myhome.spu.edu/lauw
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Expectations Show all the steps Simplify the answer. 7 minutes
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Preview The reverse of the product rule
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Derivatives and Antiderivatives
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Product Rule
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Definition of Antiderivatives
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By Definition of Antiderivatives
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Rationale The formula is useful if the integral on the right hand side is easier to evaluate than the one on the left hand side Easier Difficult
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Alternative Form
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Integration By Parts
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Example 1
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Remarks
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2. If we make a different choice such as
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Example 2
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Example 3
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Additional Formula To make calculations a bit easier, we are going to adopt the following new formula
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Example 4
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Remarks Do not use IBP for all integrals. Sometimes, Substitution is easier.
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Example 5
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Next Class Session Learn how to use a CAS (Computer Algebra System) - Maple
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