Consider a time-dependent current across a 2 \mu \mathrm{F} capacitor given as
i_{C}(t)=\left\{\begin{array}{rl}t, & 0<t<1 \mathrm{~s} \\1, & 1<t<3 \mathrm{~s} \\-t+4, & 3<t<4 \mathrm{~s} \\0, & \text { otherwise. }\end{array} \quad(\mu \mathrm{A}) .\right.Assuming v_{C}(0)=1 \mathrm{~V}, find and plot the voltage across the capacitor. In addition, find the power during 1<t<3 \mathrm{~s}, as well as the energy stored or released in this time period.