- 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 constant
being multiplied by the length of integration
- if the function is odd.
- if the function is even.
- the limits follow in a natural way.
For all
and
then
for all
All the above integrals are examples of definite integrals – having limits
and
If an integral has no limits it is called an indefinite integral and to the integral of the function
which is written
we must add an arbitrary constant, usually written
