(→Calculating the Energy of a Function) |
(→Calculating the Energy of a Function) |
||
| Line 7: | Line 7: | ||
For clarity, follow the example below. | For clarity, follow the example below. | ||
| − | <math>E=\int_{0}^{ | + | <math>E=\int_{0}^{2\pi}{|2sin(t)|^2dt}</math> |
| − | <math>E=2\int_{0}^{ | + | <math>E=2\int_{0}^{2\pi}{|sin(t)|^2dt}</math> |
Revision as of 15:56, 5 September 2008
Calculating the Energy of a Function
To calculate the energy of a function, use the following equation.
$ E=\int_{t1}^{t2}{|f(t)|^2dt} $
For clarity, follow the example below.
$ E=\int_{0}^{2\pi}{|2sin(t)|^2dt} $
$ E=2\int_{0}^{2\pi}{|sin(t)|^2dt} $
$ =\frac{1}{2}\int_0^{2\pi}(1-cos(2t))dt $
$ =\frac{1}{2}(t-\frac{1}{2}sin(2t))|_{t=0}^{t=2\pi} $
$ =\frac{1}{2}(2\pi) $
