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<math>E=\int_{0}^{5\pi} |\cos(4t)|^2\, dt</math> | <math>E=\int_{0}^{5\pi} |\cos(4t)|^2\, dt</math> | ||
| + | |||
| + | <math>E=\frac{1}{2}\int_{0}^{5\pi} |1+\cos(8t)|^2\, dt</math> | ||
| + | |||
| + | <math>E=\frac{1}{2}\times|t+\frac{1}{8}\sin(8t)|\ t = 0 to 5\pi</math> | ||
| + | |||
| + | <math>=\frac{1}{2} \times (5\pi + 0 - 0-0)</math> | ||
| + | |||
| + | <math>=\frac{5}{2}\times\pi</math> | ||
Revision as of 16:00, 4 September 2008
I assumed $ x(t)=\cos(4t) $ and time interval 0 to $ 5\pi $
Energy
$ x(t) = \cos(4t) $
$ E=\int_{t1}^{t2} |x(t)|^2\, dt $
$ E=\int_{0}^{5\pi} |\cos(4t)|^2\, dt $
$ E=\frac{1}{2}\int_{0}^{5\pi} |1+\cos(8t)|^2\, dt $
$ E=\frac{1}{2}\times|t+\frac{1}{8}\sin(8t)|\ t = 0 to 5\pi $
$ =\frac{1}{2} \times (5\pi + 0 - 0-0) $
$ =\frac{5}{2}\times\pi $
