7-2 Antidifferentiation by substitution

An indefinite integral with respect to x is *Notes: A definite integral is a number An indefinite integral is a family of functions Ex 1) Evaluate

Review of Some Important Antiderivatives Properties Power Formulas

Review of Some Important Antiderivatives Trigonometry Exponents & Logarithmic

Note: WE have to be REALLY CAREFUL of what the question is asking *Note: WE have to be REALLY CAREFUL of what the question is asking! WATCH THE NOTATION! Ex 3) Let f (x) = x3 + 1 and let u = x2. Find each of the following antiderivatives in terms of x.

Substitution A complete substitution will take and change it to The goal is to look for something that is the derivative of something else in the problem This takes practice! Be patient with yourself as you learn how to do these. Ex 4) Evaluate Let u = cos x du = –sin x dx –1du = sin x dx

Ex 5) Evaluate Ex 6) Evaluate

Evaluating Definite Integrals *Note: If you adjust limits – you don’t have to substitute back Ex 8)

Ex 9) Evaluate

homework Pg. 342 #1 – 43 (mult of 1+3n), 53 – 61 odd