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The Definite Integral

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The Definite Integral

Section 14.3

- 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:

- 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

- Find the exact value of
Draw a picture!

- A = ½ (f(3) + f(12))∙ 9
- f(12) = 97, f(3) = 43

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

a.

b.

Evaluateitat the upper and lowerbound. Then, subtract!

- Find the exact value of

- Find the exact value of

- Calculate:
- This one is a little harder to integrate, so draw a picture!

¼ (10 * 50) π

125 π

Pages 831 – 832

3 – 14

#10 is extra credit