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Definite Integrals

Definite Integrals. 5.6 “u” substitution. The First Fundamental Theorem of Calculus. To understand this, lets do a problem in 2 steps: Find F(x): Find F’(x) . The First Fundamental Theorem of Calculus. If f is continuous on [a,b] then is differentiable on

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Definite Integrals

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  1. Definite Integrals 5.6 “u” substitution

  2. The First Fundamental Theorem of Calculus To understand this, lets do a problem in 2 steps: • Find F(x): • Find F’(x)

  3. The First Fundamental Theorem of Calculus If f is continuous on [a,b] then is differentiable on every point in [a,b] and

  4. Rules

  5. Examples – Find dF/dx

  6. u substitution We’ve talked about this a little; as you substitute “u” in, the limits of integration will change. Lets look at a few examples to see how these work:

  7. Examples

  8. Do you have to do this? No, you don’t. It just sometimes makes some very unwieldy problems look nicer and simplify quicker.

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