Properties of Definite Integrals

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Presentation transcript:

Properties of Definite Integrals

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.)

IF f(x) is EVEN and the bounds are opposites. 6. IF f(x) is ODD and the bounds are opposites. 7. Recall: f(x) is EVEN if f(-x) = f(x) f(x) is ODD if f(-x) = -f(x)