5.5 indefinite integrals always add an arbitrary constant “c” to indicate a family of solutions
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
BYSUBSTITUTION
THE CHAIN RULE
THIS IS BIG
REMEMBER
There are no product or quotient rules for integration.
5.7 Trapezoidal RuleEstimate area for function with no
antiderivative
Trapezoids give better approximation than rectangles
Fit the curve betterCan use fewer trapezoids than
rectangles
Simpson’s RuleUses 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