5.6 integration by substitution method (u-substitution) thurs feb 20
DESCRIPTION
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 . - PowerPoint PPT PresentationTRANSCRIPT
5.6 Integration by Substitution Method (U-substitution)
Fri Feb 5Do 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
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 due Monday, 1-89 AOO due Tuesday
5.6 U-Substitution Review / Practice
• Do Now• Evaluate the integrals• 1)
• 2)
HW Review: p.333 1-89
Practice
• Worksheet if time
Closure
• Evaluate the integral
• HW: p.333 #1-89 AOO
5.6 Substitution MethodTues Feb 9
• Evaluate the integral using substitution
HW Review: p.333 1-89
Practice
• Worksheet
Closure
• When do we use substitution when integrating? How does it work? What about with definite integrals?
• HW: none