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4.5 Integration By Pattern Recognition

A Mathematics. Academy. Production. 4.5 Integration By Pattern Recognition . Integration by Pattern Recognition:. The first basic type of integration problem is in the form: . Integrate by recognizing the Pattern. Note: If . Then. Integrating we get:. Therefore, this integral

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4.5 Integration By Pattern Recognition

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  1. A Mathematics Academy Production 4.5 Integration By Pattern Recognition

  2. Integration by Pattern Recognition: The first basic type of integration problem is in the form:

  3. Integrate by recognizing the Pattern Note: If Then Integrating we get: Therefore, this integral is of the type: But, Substitute, Henceforth,

  4. Then Note: If Note: This is exactly in the form! Therefore, this integral is of the type: Integrating we get: But, Substitute, Henceforth,

  5. Multiplying by a Form of 1 to integrate: Then Note: If Note: This is not exactly in the form! The inside of the Integral has to be multiplied by 2 Therefore the outside of the Integral has to be multiplied by ½, since( 2) (½) = 1, and as long as we multiple the entire integral by a numeric form of 1 we can proceed with integration.

  6. Now multiply by a form of 1 to integrate: Then Note: If Note: This is exactly in the form! Integrate this form to get Simplifying to get Substitute get

  7. Integrate Sub to get Integrate Back Substitute

  8. Ex. Evaluate Pick u, compute du Sub in Integrate Sub in

  9. Trig Integrals in the form: Then Let Note: This is exactly in the form! Integrate this form to get Sub in

  10. Basic Trig Integrals

  11. The key to each basic Trig Integral is that: First make sure you do not have a problem. Let u = The angle While du = The derivative of the angle You need to know the 6 trig. Derivatives, so that you can work backwards and find their Anti-derivatives!

  12. Using the Trig Integrals • The technique is often to find a u which is the angle, the argument of the trig function • Consider • What is the u, the du? • Substitute, integrate

  13. Let u = x3 ; du = 3x2dx ; C.F. 1/3

  14. Symmetry in Definite Integral Integrals of Symmetric Functions

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