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Is there a simpler way of solving this then calculating

x1(h)+x2(h)+x3(h)+x4(h) by using the given y values (in this case h, the height is one, because the length of each rectangle is one)

because it could take a while if the heights were all different, and there were many more rectangles... is there a CAS (calculator/graphing) method... something more efficient.

Can you calculate L/R area approximation using a formula, without drawing the graph.. so imagine the graph wasn't part of the question... could you solve this alternatively with a formula?

Does anyone have an efficient method to solve L/R area approximation

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I don't know of any CAS method but if you have infinitely many rectangles, then you can use integral calculus which may not be less complicated all the time but will probably be less tedious (which is what I think you mean when you say "more simple"). However calculus will give you an exact answer and isn't an approximation. You can use calculus without drawing a graph.

If instead of rectangles you use trapeziums, then you can use what is aptly known as the trapezium rule, which has a formula. However the formula is not really simpler than the rectangle one. This will give you an approximate answer but it will be more accurate than rectangles. You could use the formula without drawing a graph. You could approximate from the left and right using this technique.

As an aside you probably wouldn't use rectangles of different values of h because that would just make your life more computationally difficult.

So in terms of L/R stuff the trapezium rule is probably your best bet. I hope this helps.

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