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5.5 INDEFINITE INTEGRALS

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.

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5.5 INDEFINITE INTEGRALS

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  1. 5.5 INDEFINITE INTEGRALS ALWAYS ADD AN ARBITRARY CONSTANT “C” TO INDICATE A FAMILY OF SOLUTIONS.

  2. Antiderivative aka indefinite integral NO limits of integration are used

  3. We already know lots of integrals

  4. New Integrals

  5. 5.5 Initial Value Problems YES, WE HAVE DONE THESE

  6. 5.5 Initial Value Problems YES, WE HAVE DONE THESE SO THEY’LL BE EASY!

  7. 5.6 INTEGRATION BYSUBSTITUTIONTHE CHAIN RULETHIS IS BIG

  8. REMEMBER There are no product or quotient rules for integration.

  9. 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

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

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

  12. Sail through this test • Don’t go overboard

  13. Chain Rule • Trapezoidal approx • Simpson’s approx • NINT

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