Question

Find the charge flowing q(t) through a device if the current is i(t) = 10 e-30t sin 40t A,

q(0) = 0

Answer 1

$$q(t)=10\int^t_0e^{-30t}\sin(40t)\text dt,\\\space\\ \bigg>\int u\text dv=uv-\int v\text du\bigg>\\\space\\ >u=\sin(40t),\space \text dv=e^{-30 t}>\\\space\\ \text du=40\cos(40t),\space v=\dfrac{e^{-30t}}{-30},\\\space\\ q(t)=10\bigg[\dfrac{\sin(40y)e^{-30t}}{-30}\bigg|^t_0-\int\dfrac{e^{-30t}}{-30}40\cos(40t)\text dt.\bigg]$$