Definite Integrals

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

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Rules
5
Examples Find dF/dx

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u substitution

• Weve 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 dont. It just sometimes makes some very
  unwieldy problems look nicer and simplify
  quicker.