Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 442: 83



Work Step by Step

The total energy stored in a capacitor is given by: $W=\int_0^{\infty} P(t) \ dt \\=\int_0^{\infty} \dfrac{v^2}{R} (e^{-t/RC}-e^{-2t/RC}) \ dt \\=\dfrac{v^2}{R}(-RCe^{-t/RC} +\dfrac{RC}{2} e^{-2t/RC})|_0^{\infty}\\=\dfrac{V^2}{R} (\dfrac{RC}{2})\\=\dfrac{1}{2}CV^2$
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