4012 u-du : Integrating Composite Functions AP Calculus.

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Presentation transcript:

4012 u-du : Integrating Composite Functions AP Calculus

Trig Functions

auau

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

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

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

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

Change of Boundaries

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

EX: Change of Variables ln

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

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.