The definite integral
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The Definite Integral. Section 14.3. Definite integral. As the number of integrals increase while doing the Riemann sum, the answer becomes more accurate. The limit of the Riemann Sum is called the definite integral of f from a to b, written:. Example 1.

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The Definite Integral

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The definite integral

The Definite Integral

Section 14.3


Definite integral

Definite integral

  • As the number of integrals increase while doing the Riemann sum, the answer becomes more accurate. The limit of the Riemann Sum is called the definite integral of f from a to b, written:


Example 1

Example 1

  • Use integral notation to express the area of the region bounded by the x-axis, the graph of g(x) = 5x5 – 3x4 and the lines x = 10 and x = 25


Example 2

Example 2

  • Find the exact value of

    Draw a picture!


Trapezoid with a b 1 b 2 h

Trapezoid with A = ½ (b1 + b2)h

  • A = ½ (f(3) + f(12))∙ 9

  • f(12) = 97, f(3) = 43


The anti derivative

The Anti-derivative

  • This is exactly the opposite of the derivative. We have to ask ourselves, what number will give us this derivative.


Try some others

Try some others!

a.

b.


Once we find the anti derivative

Once we find the anti-derivative..

Evaluateitat the upper and lowerbound. Then, subtract!


Back to example 2

Back to example 2!

  • Find the exact value of


Example 3

Example 3

  • Find the exact value of


Example 4

Example 4

  • Calculate:

  • This one is a little harder to integrate, so draw a picture!


Example 41

Example 4

¼ (10 * 50) π

125 π


Homework

Homework

Pages 831 – 832

3 – 14

#10 is extra credit


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