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# Integration by Parts - PowerPoint PPT Presentation

Integration by Parts. Method of Substitution Related to the chain rule Integration by Parts Related to the product rule More complex to implement than the Method of Substitution. Derivation of Integration by Parts Formula. Let u and v be differentiable functions of x .

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## PowerPoint Slideshow about 'Integration by Parts' - malory

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Presentation Transcript

• Method of Substitution

• Related to the chain rule

• Integration by Parts

• Related to the product rule

• More complex to implement than the Method of Substitution

Let u and v be differentiable functions of x.

Let u and v be differentiable functions of x.

(Product Rule)

Let u and v be differentiable functions of x.

(Product Rule)

(Integrate both sides)

Let u and v be differentiable functions of x.

(Product Rule)

(Integrate both sides)

(FTC; sum rule)

Let u and v be differentiable functions of x.

(Product Rule)

(Integrate both sides)

(FTC; sum rule)

Let u and v be differentiable functions of x.

(Product Rule)

(Integrate both sides)

(FTC; sum rule)

(Rearrange terms)

• What good does it do us?

• We can trade one integral for another.

• This is only helpful if the integral we start with is difficult and we can trade it for a good (i.e., solvable) one.

• For u, choose a function whose derivative is “nicer”.

• LIATE

• dv must include everything else (including dx).