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<math>E=\int_3^{5}{\dfrac{2t}{t^2+5}dt}</math> | <math>E=\int_3^{5}{\dfrac{2t}{t^2+5}dt}</math> | ||
| + | |||
| + | <math>U=t^2+5</math> <math>U(3)=3^2+5=9+5=14</math> | ||
| + | |||
| + | <math>dU=2tdt</math> <math>U(5)=5^2+5=25+5=30</math> | ||
| + | |||
| + | |||
| + | <math>E=\int_14^{30}{\dfrac{du}{U}</math> | ||
| + | |||
| + | <math>E=\ln U |_{U=14}^{U=30}</math> | ||
| + | |||
| + | <math>E=\ln 30 - \ln 14</math> | ||
| + | |||
| + | <math>E=\ln {30/14)</math> | ||
Revision as of 14:28, 4 September 2008
Compute the Energy and Power of the signal $ x(t)=\dfrac{2t}{t^2+5} $ between 3 and 5 seconds.
Energy
$ E=\int_3^{5}{\dfrac{2t}{t^2+5}dt} $
$ U=t^2+5 $ $ U(3)=3^2+5=9+5=14 $
$ dU=2tdt $ $ U(5)=5^2+5=25+5=30 $
$ E=\int_14^{30}{\dfrac{du}{U} $
$ E=\ln U |_{U=14}^{U=30} $
$ E=\ln 30 - \ln 14 $
$ E=\ln {30/14) $
