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5.6 Integration by Substitution Method (U-substitution) Thurs Feb 20. Do Now Find the derivative of. HW Review: p.326. 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 .
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5.6 Integration by Substitution Method (U-substitution)Thurs Feb 20 Do Now Find the derivative of
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.333-335 #1-89 EOO
5.6 U-Substitution Review / PracticeFri Feb 21 • Do Now • Evaluate the integrals • 1) • 2)
Practice • Worksheet if time
Closure • Evaluate the integral • HW: p.333 #1-89 AOO
5.6 Substitution MethodMon Feb 24 • Evaluate the integral using substitution
Practice • Worksheet
Closure • When do we use substitution when integrating? How does it work? What about with definite integrals? • HW: none