Indefinite Integrals

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```					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

give better approximation than rectangles  Fit the curve better  Can use fewer trapezoids than rectangles

 Trapezoids

Simpson’s Rule
 Uses  “n”

parabolas to approximate the area

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


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