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The Definite Integral - PowerPoint PPT Presentation

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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Presentation Transcript

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!

Trapezoid with A = ½ (b1 + b2)h

• 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