
Numerical Techniques:
Numerical
Differentiation and
Integration
Dr. Cem Özdo
˘
gan
LOGIK
Numerical
Differentiation and
Integration with a
Computer
Variable force in one
dimension
Differentiation with a
Computer
Simple Pendulum
Numerical Integration - The
Trapezoidal Rule
The Composite
Trapezoidal Rule
5.24
Numerical Integration - The Trapezoidal Rule II
•
Is there any way that the definite integral can be found
when the antiderivative is unknown?
•
We can do it numerically by using the composite
trapezoidal rule
•
The definite integral is the area between the curve of f (x)
and the x-ax is.
•
That is the principle behind all numerical integration;
Figure: The trapezoidal rule.
•
We divide the distance from
x = a to x = b into vertical
strips and
add the areas of these strips.
•
The strips are often made
equal i n widths but that is not
always required.
•
Approximate the curve with a
sequence of straight l ines
.
•
In effect, we slope the top of
the strips t o match with the
curve as best we can.
•
The gives us the trapezoidal rule. Figure illustrates this.