Advanced Placement Calculus BC March 28-29, 2018 Mrs. Agnew Integration by parts Advanced Placement Calculus BC March 28-29, 2018 Mrs. Agnew

Essential Question Essential Vocabulary How do you integrate functions using the integration by parts technique? Essential Vocabulary Integration by Substitution Integration by Parts Definite Integral Indefinite Integral

Integration Techniques There are a variety of differentiation techniques… which require a variety of ANTI-differentiation techniques Chain Rule corresponds to _____________ Product Rule corresponds to ___________

Integration by Parts Rearranging the previous equation, we get: Then substituting u = f(x) and v = g(x), we can derive the formula for INTEGRATION BY PARTS:

Hints for use The goal is to derive a simpler integral than the one we started with. Make sure that the function you assign u gets simpler when differentiated and that dv can be easily integrated to find v. It may be necessary to use integration by parts twice. LIATE = Log, Inverse, Algebraic, Trig, Exponential Priority for selecting “u”

Guided practice Guided practice: page 401 #2 – 14 (Even) Evaluating Definite Integrals: Page 401 #16 – 24 (Even)

Homework: page 401 – 402 #3, 7, 11, 13, 17, 21, 25, 27, 41