Trapezoidal Rule
Contents
Trapezoidal Rule#
For the trapezoidal rule we approximate the integral of
and calculating it’s area.
The area of the trapezium is given by:
In the case where
In the case where
which is the same as above, so in general we can approximate the integral as:
Composite Trapezoid Rule#
Now, if we were to break up this interval into
To calculate this we use the sum:
where
we can therefore write the approximation as:
note how each
For a choice of
Composite Trapezoidal Rule with a Discrete Data Set#
Again, consider the data set
If we wanted to approximate the integral of this data set using the trapezoidal rule, we can apply this to each interval individually:
If the
References#
- IntTrap1
James F. Epperson. An Introduction to Numerical Methods and Analysis. John Wiley & Sons, Inc., Hoboken, New Jersey, second edition edition, 2013.