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4.1 Antiderivatives and Indefinite Integration

Learning Goals: We are learning about: Antiderivatives Notation for Antiderivatives Basic Integration Rules Initial Conditions and Particular Solutions Why are we learning this? Helps us find useful formulas! (Example 8)

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Antiderivatives: Find a function F whose derivative is:

Now find another function!

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Antiderivatives

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Example 1: Solving a Differential Equation

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Notation for Antidertivative: Antidifferentiation/Indefinite Integration Antiderivative/Indefinite Integral Need to find the y that makes the equation true. Once we know the y what are we doing to it?

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Basic Integration Rules

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Example 2: Applying The Basic Integration Rules

Example 3: Rewriting Before Integrating

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Example 5: Rewriting Before Integrating – We have no Quotient Rule

Same applies with derivatives

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Example 6: Rewriting Before Integration Using Trig Identities

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Example 7: Finding a Particular Solution

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Remember we need to rewrite the integrand to fit the basic integration rules:

How does this show that integration is limited compared to differentiation?

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Example 8 – Great Example. Read Together. 4

Example 8 – Great Example!! Read Together. 4.1 Hmwr: 1-13odd, 17, 19, 23, 25, 29-45odd, 51, 57, 67

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