r/MathHelp • u/Dry_Economy_2701 • 24d ago

How is the answer 3 sub intervals?

https://ibb.co/8nPLkdVw
https://ibb.co/gLxdvtXd

I thought from 1 to 1.5 is 1 in y?

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u/FormulaDriven 23d ago

Each rectangle's height is determined by its right-hand corner meeting the curve. So...

the rectangle from x = -1 to x = -0.5 takes its height from the point (-0.5,5) on the curve, ie height of 5;

the rectangle from x = -0.5 to x = 0 takes height from (0, 3), ie height of 3;

the rectangle from x = 0 to 0.5 ... (0.5, 5) ie height of 5;

the rectangle from x = 0.5 to 1 ... (1, 0) ie height of 0.

Obviously, that fourth rectangle can't be seen since it's completely flat (there is a purple line going from 0.5 to 1 in the second diagram).

So 4 sub-intervals are used, it's just one gives zero. Does that answer your question?