Does the left riemann sum underestimate or overestimate the area of the region under the graph of a positive increasing function?
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my book says it will be an overestimate
The right Riemann sum is the one that overestimates, if f is a positive increasing function.
Are you sure? Double check that answer. @blockcolder diagram is perfect, you can see it will underestimate.
No the question I typed is exaclty as is in the book, maybe my book is wrong
Yes, maybe. It's certainly been known to happen. :) I wasn't questioning whether the question was stated correctly, just making sure you are looking at the right answer in the back (they are usually very jammed up on the page, it's easy to be looking for #37 and accidentally look at #39, lol). :)
so if they asked: does the right riemann sum give an overestimate or underestimate or a postive deacring function. Then the answer would be understand right?
If you draw it, you should see the answer.
it underestimates it?
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Math books often have typos or mistakes. A bad math book will have an annoyingly large number of mistakes/typos.
Here is a picture of a left Riemann sum for a curve that increases