Integral derivation of capacitor solar container formula

This behavior is predicted by the integral form of the capacitor i i - v v equation. The usual capacitor i i - v v equation is i i as a function of v v in derivative form, i = C d v d t i = C dtdv C C is the capacitance, a physical property of the capacitor. Lets consider the equation which defines the voltage across and inductor V (t) = L* di/dt so if L = 1 we have: For a capacitor I (t) = C * dv/dt, if C = 1 we have: So if we define the voltage or current through or across an inductor or capacitor it will give us the integral or derivative depending. Here is the process they followed from the textbook My confusion is: when the initial voltage across the capacitor is not able to be discerned, that it is "mathematically convenient to set t0 = −∞ and v (−∞) = 0" Why would t0 be set to −∞ and wouldn't v (−∞) = −∞ not 0? Has there been a finite. The capacitor energy storage formula explains how capacitors store electrical energy using voltage and capacitance.