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