5.6 integration by substitution method (u-substitution) thurs dec 3 do now find the derivative of
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Reverse Chain Rule Looking at the 2 Do Now problems, we can say Notice how 2 factors integrate into oneTRANSCRIPT
5.6 Integration by Substitution Method (U-substitution)Thurs Dec 3
Do NowFind 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.333-335 #9 13 20 31 43 53 59 67 69 74 81 89 95
5.6 U-Substitution Review / PracticeWed Feb 11
• Do Now• Evaluate the integrals• 1)
• 2)