We have to integrate
functions of the form
.
The rule here is to add one to the power and divide by the new power,
never forgetting that we must add a constant.
.
The rule here is to add one to the power and divide by the new power,
never forgetting that we must add a constant.
This extends to any
combination of sums and multiples of powers of
For
example, remembering that
For
example, remembering that
which
may be simplified further.
This adding of one to the
power and dividing by the new power generalises to fractional and
negative powers. For example,
If we have limits, values of
between
which the integral takes place, then the answer is just a number.
between
which the integral takes place, then the answer is just a number.
If the integral has limits
then we have no need for C, since we have C from the first bracket
take C from the second bracket.
There is once case where the
above rule does not work.
We
cannot divide by zero but we can still evaluate the integral. This is
a special case:
.
We discuss logs and natural logs in C2
- Logarithms.
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