hi,
>> How do we calculate the area of an exponential curve?
To calculate the energy stored in the inductor, you use the integration formula for calculus,
to get the area under the curve, from t0 to tmax.
Use the same method to find the area under any 'curve'.
If you just want a close approximation, you could plot the curve on graph paper,,, and use Simpsons rule,,,
that is finding the sum of the area's of rectangles, drawn on the graph.
Is this any clearer?