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<math>E=16*\int_2^6 sin(12\pi t)^2 dt</math> | <math>E=16*\int_2^6 sin(12\pi t)^2 dt</math> | ||
| − | <math>E=16*(\dfrac{ | + | <math>E=16*(\dfrac{12 \pi t}{2}-\dfrac{sin(2*(12\pi t))}{4})\mid_2^6</math> |
| − | <math>E= | + | <math>E=16*(6\pi t-\dfrac{sin(24\pi t)}{4})\mid_2^6</math> |
| − | <math>E= | + | <math>E=96\pi *t-\dfrac{16sin(24\pi *t)}{4}\mid_2^6</math> |
| − | <math>E= | + | <math>E=96\pi *6-\dfrac{16sin(24\pi *5)}{4}-(96\pi *2-\dfrac{16sin(24\pi *1)}{4}</math> |
| − | <math>E= | + | <math>E=384\pi</math> |
Revision as of 08:17, 5 September 2008
Given the Signal x(t) = 4sin(2 * pi * 6t), Find the energy and power of the signal from 2 to 6 seconds.
Energy
$ E=\int_2^6 |x(t)|^2 dt $
$ E=\int_2^6 |4sin(12\pi t)|^2 dt $
$ E=16*\int_2^6 sin(12\pi t)^2 dt $
$ E=16*\int_2^6 sin(12\pi t)^2 dt $
$ E=16*(\dfrac{12 \pi t}{2}-\dfrac{sin(2*(12\pi t))}{4})\mid_2^6 $
$ E=16*(6\pi t-\dfrac{sin(24\pi t)}{4})\mid_2^6 $
$ E=96\pi *t-\dfrac{16sin(24\pi *t)}{4}\mid_2^6 $
$ E=96\pi *6-\dfrac{16sin(24\pi *5)}{4}-(96\pi *2-\dfrac{16sin(24\pi *1)}{4} $
$ E=384\pi $
