Presentation on theme: "4.5 Integration By Pattern Recognition"— Presentation transcript:
1 4.5 Integration By Pattern Recognition A MathematicsAcademyProduction
2 Integration by Pattern Recognition: The first basic type of integrationproblem is in the form:
3 Note: If Integrate by recognizing the Pattern Then Integrating we get: Therefore, this integralis of the type:Substitute,But,Henceforth,
4 Note: This is exactly in the form! ThenNote: IfNote: This is exactly in the form!Therefore, this integralis of the type:Integrating we get:Substitute,But,Henceforth,
5 Note: This is not exactly in the form! Multiplying by a Form of 1 to integrate:ThenNote: IfNote: This is not exactly in the form!The inside of the Integral has to be multiplied by 2Therefore the outside of the Integral has to bemultiplied by ½, since( 2) (½) = 1, and as long as we multiple the entire integral by a numeric form of 1we can proceed with integration.
6 Note: This is exactly in the form! Now multiply by a form of 1 to integrate:Note: IfThenNote: This is exactly in the form!Integrate this form to getSimplifying to getSubstitute get
11 The key to each basic Trig Integral is that: First make sure you do not have a problem.Let u = The angleWhile du = The derivative of the angleYou need to know the 6 trig. Derivatives,so that you can work backwards and findtheir Anti-derivatives!
12 Using the Trig Integrals The technique is often to find a u which is the angle, the argument of the trig functionConsiderWhat is the u, the du?Substitute, integrate