Definite Integrals 5.6 “u” substitution.

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Presentation transcript:

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 every point in [a,b] and

Rules

Examples – Find dF/dx

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:

Examples

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