1. Reversing the limits changes the sign. 2.

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Presentation transcript:

Page 269 gives rules for working with integrals, the most important of which are: 1. Reversing the limits changes the sign. 2. If the upper and lower limits are equal, then the integral is zero. 3. Constant multiples can be moved outside.

Reversing the limits changes the sign. 1. If the upper and lower limits are equal, then the integral is zero. 2. Constant multiples can be moved outside. 3. 4. Integrals can be added and subtracted.

4. Integrals can be added and subtracted. 5. Intervals can be added (or subtracted.)

The average value of a function is the value that would give the same area if the function was a constant:

The mean value theorem for definite integrals says that for a continuous function, at some point on the interval the actual value will equal to the average value. Mean Value Theorem (for definite integrals) If f is continuous on then at some point c in , p