Solve the Problem $\mathrm { q }$ (In Coulombs) Delivered by a Current

Multiple Choice

Solve the problem.
-The charge $\mathrm { q }$ (in coulombs) delivered by a current $\mathrm { i }$ (in amperes) is given by $\mathrm { q } = \int \mathrm { i } \mathrm { dt }$ , where $t$ is the time (in seconds) . A damped-out periodic wave form has current given by $\mathrm { i } = \mathrm { e } ^ { - 3 \mathrm { t } } \cos 5 \mathrm { t }$ . Find a formula for the charge delivered over time $t$ .

A) $\frac { e ^ { - 3 t } ( - 3 \cos 5 t + 5 \sin 5 t ) } { 25 } + C$
B) $\frac { e ^ { - 3 t } ( - 3 \cos 5 t + \sin 5 ) } { 34 } + C$
C) $\frac { e ^ { - 3 t } ( - 3 \cos 5 t + 5 \sin 5 t ) } { 34 } + C$
D) $\frac { - 3 \cos 5 t + 5 \sin 5 t } { 34 } + C$