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2413 Calculus I Chapter 5(5) Integration by Substitution

2413 Calculus I Chapter 5(5) Integration by Substitution. Substitution is how we integrate something that came from a chain rule problem. Take the derivative of:. Inside function. Derivative of inside.

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2413 Calculus I Chapter 5(5) Integration by Substitution

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  1. 2413 Calculus IChapter 5(5)Integration by Substitution

  2. Substitution is how we integrate something that came from a chain rule problem. Take the derivative of: Inside function Derivative of inside Note: You know substitution is needed when the integral contains an inside and an outside function.

  3. Steps for Integration by Substitution u du Take the derivative and that is du Identify the inside function and call it u Re-write the integral substituting u & du Integrate: Substitute x back in:

  4. Substitution – Extra or missing constants Extra Constants Identify u Find du Substitute u & du Integrate Substitute back

  5. Identify u Find du Substitute u & du Integrate Substitute back

  6. Substitute u & du Integrate Substitute back

  7. Substitution – Extra variables Identify u Find du Extra variable Substitute u & du Integrate Substitute back

  8. Substitution – Definite Integrals Identify u Find du Substitute u & du and change integral # Integrate Evaluate

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