Properties of Integration
- 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