Properties of Integration

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– interchanging the limits changes the sign of the integral.

– an integral can be factorised with a constant.

– if the limits are the same, the integral is zero.

– the integral of the sum of two functions is the sum of the integrals.

– integrating a constant results in the constantbeing multiplied by the length of integration

– if the function is odd.

– if the function is even.

– the limits follow in a natural way.

For allandthenfor all

All the above integrals are examples of definite integrals – having limitsandIf an integral has no limits it is called an indefinite integral and to the integral of the functionwhich is writtenwe must add an arbitrary constant, usually written

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