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How can the energy involved in a circuit be calculated? Could it be calculated as the area under the power curve? Please help me, because I can't find the way to calculate AREA UNDER THE POWER CURVE.

After you plot the power as an expression such as P(R1), notice the legend in the corner of the plot window. Right-click on the legend entry for the appropriate trace, and you'll see a context menu. One of the options should be "Plot P(R1) integral" which should do exactly what you're looking for.