5.5 INDEFINITE INTEGRALS ALWAYS ADD AN ARBITRARY CONSTANT “C” TO INDICATE A FAMILY OF SOLUTIONS.

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Presentation transcript:

5.5 INDEFINITE INTEGRALS ALWAYS ADD AN ARBITRARY CONSTANT “C” TO INDICATE A FAMILY OF SOLUTIONS.

Antiderivative aka indefinite integral NO limits of integration are used

We already know lots of integrals

New Integrals

5.5 Initial Value Problems YES, WE HAVE DONE THESE

5.5 Initial Value Problems YES, WE HAVE DONE THESE SO THEY’LL BE EASY!

5.6 INTEGRATION BY SUBSTITUTION THE CHAIN RULE THIS IS BIG

REMEMBER There are no product or quotient rules for integration.

5.7 Trapezoidal Rule  Estimate area for function with no antiderivative  Trapezoids give better approximation than rectangles  Fit the curve better  Can use fewer trapezoids than rectangles

Simpson’s Rule  Uses parabolas to approximate the area  “n” must be even

Estimate the error that occurs when using Trapezoidal Rule and Simpson’s Rule

 Sail through this test  Don’t go overboard

 Chain Rule  Trapezoidal approx  Simpson’s approx  NINT