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Integral Calculus in AE

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I'm wondering if there is a way to add the values of a property for every frame before the current time indicator?

 

the relevance to calculus:

 

I'm wondering if there is a procedural way in after effects to calculate the area under a curve for a property (integrating the function from "time a" to "time b"). for instance, if you had a slider that you keyframed to have a value of 1 for 3 seconds, a value of 10 for 1 second, and again a value of 1 for 3 seconds (with Hold Keyframe on in this example, but not necessarily so in all other instances). after the 7 seconds in the example, the area under the curve (finite integral from "time 0" to "time 7") should have a value of 16 (if i did my math correctly)

if there is a way to do this, will it work on, for instance, a slider with key frames like the one above, with NO Hold Keyframes, and with easy ease applied to the keyframes? essentially, could it work on any property with any shaped curve?

thanks, i hope i didnt confuse people too much with my question


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