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The Definite Integral

The Definite Integral. Section 6.6. The Definite Integral. If a function f is continuous on an interval [ a,b ], then f is integrable on [ a,b ], and the net signed area A between the graph of f and the interval [ a,b ] is

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The Definite Integral

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  1. The Definite Integral Section 6.6

  2. The Definite Integral If a function f is continuous on an interval [a,b], then f is integrable on [a,b], and the net signed area A between the graph of f and the interval [a,b] is This is called the definite integral of f from a to b. The numbers a and b are called the lower limit of integration and the upper limit of integration, respectively.

  3. Fundamental Theorem of Calculus If f is continuous on [a,b] and F is any anti-derivative of f on [a,b], then

  4. Fundamental Theorem of Calculus If f is continuous on [a,b] and F is any anti-derivative of f on [a,b], then

  5. Fundamental Theorem of Calculus If f is continuous on [a,b] and F is any anti-derivative of f on [a,b], then

  6. Examples • Evaluate • Evaluate

  7. More Examples • Evaluate • Evaluate

  8. Practicepg. 406 (9-25)No “u” substitutions required

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