The current through a $\backslash (20\backslash$mu $\backslash$mathrm$\{$~F$\}\backslash )$ capacitor is shown below.

a$)$ Find and sketch the voltage across the capacitor as a function of time from $0$ to $65$ s $,$ assuming $\backslash ($ v$(0)=0\backslash ).$

b$)$ Compute voltage across the capacitor at $\backslash ($ t$=60\backslash$mathrm$\{$~s$\}\backslash )($do not estimate this value from the graph, but find a precise answer analytically$).$