Can Geometry Always Determine Voltage from Current Graphs in Circuit Analysis?

[theman408]

Homework Statement

In my Engineering Circuit Analysis I class I am in Capacitors and Inductors where they give us the graph of either i(t) or v(t) and we have to determine the graph of current or voltage depending if it's a capacitor or inductor.

Homework Equations

For example,
v(t)= L di/dt is the differential equation used and if you integrate it you get the current equation for the inductor.

The Attempt at a Solution

My question is, if you have a graph say current for a capacitor and ur asked to determine the graph of voltage for it, When cannot i not use the Geometry to determine the integration? When is that i have to use the slope-point equation to determine the line equation.?

My professor told me that i can use 1/2 base height or base height if it was geometrically possible to agilize the problem but sometimes it wasn't that straight forward, therefore i have to determine the equation so i can integrate it.

 

[Redbelly98]

You can use geometry to get the integral when the graph happens to be a simple geometric figure, such as a triangle or rectangle.

If the graph is more complex in form, you would need to deal with the equation for the graph in order to get the integral.