5.6 Integration by Substitution Method (U-substitution) Thurs Dec 3 Do Now Find the derivative of

HW Review

Reverse Chain Rule Looking at the 2 Do Now problems, we can say Notice how 2 factors integrate into one

Substitution Method If F’(x) = f(x), then

Integration by Substitution (U-Substitution) 1) Choose an expression for u – Expressions that are “inside” another function 2) Compute 3) Replace all x terms in the original integrand so there are only u’s 4) Evaluate the resulting (u) integral 5) Replace u after integration

Expressions for U-substitution Under an exponent Inside a function (trig, exponential, ln) In the denominator The factor in a product with the higher exponent Remember: you want to choose a U expression whose derivative will allow you to substitute the remainder of the integrand!

Ex1 Evaluate

Ex 2 – Multiplying du by constant Evaluate

Ex 3 – u in the denominator Evaluate

Ex 4 - Trig Evaluate

Ex 5 – Integrating tangent Evaluate

Ex 6 – 2 step Substitution Evaluate

Substitution and Definite Integrals When using u-substitution with definite integrals you have 2 options – Plug x back in and evaluate the bounds that way – Change the x bounds into u bounds and evaluate in terms of u

Ex Evaluate

Closure Evaluate the integral HW: p #

5.6 U-Substitution Review / Practice Wed Feb 11 Do Now Evaluate the integrals 1) 2)