Question
In a problem in electrical theory, the integral $\int_{0}^{\infty} R i^{2} d t$ occurs, where the current $i=I e^{-R t / L}, t$ is time, and $R, I,$ and $L$ are positive constants. Find the integral.
Step 1
This gives us: \[ \int_{0}^{\infty} R (I e^{-R t / L})^{2} d t = \int_{0}^{\infty} R I^{2} e^{-2 R t / L} d t \] Show more…
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