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4012 u-du : Integrating Composite Functions AP Calculus.

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Presentation on theme: "4012 u-du : Integrating Composite Functions AP Calculus."— Presentation transcript:

1 4012 u-du : Integrating Composite Functions AP Calculus

2 Trig Functions

3 auau

4 Formal Change of Variables > Solve for x in terms of u ILL: Let then and becomes Review: Antiderivatives

5 Formal Change of Variables > Rewrite in terms of u - du

6 Formal Change of Variables > Rewrite in terms of u - du

7 Formal Change of Variables > Rewrite in terms of u - du NEW :Definite Integrals

8 Change of Boundaries

9 Formal Change of Variables > Rewrite in terms of u - du NEW :Definite Integrals

10 EX: Change of Variables ln

11 Formal Change of Variables > Solve for x in terms of u

12 Complete Change of Variables > At times it is required to even change the du as the u is changed above. We will solve this later in the course.


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