The lower bound should be 1 since the summation starts at 1, but everything else looks fine.I was reviewing past exams and this problem was given:
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Is it right to say that the integral is [imath]\int_{0}^{10000} \sqrt{x} dx[/imath]? Or is my integral wrong?
Thank you!The lower bound should be 1 since the summation starts at 1, but everything else looks fine.
I'm not so sure of that. But do we want an under- or over-estimate?The lower bound should be 1 since the summation starts at 1, but everything else looks fine.
hm...I need to review my Riemann Sum definition and give this some thought.I'm not so sure of that. But do we want an under- or over-estimate?
hm...I need to review my Riemann Sum definition and give this some thought.
Good explanation.This can be remembered by thinking about an extreme case like [imath]\sum_{i=1}^1\sqrt{i}[/imath] which equals 1.
This wouldn't make sense as [imath]\int_1^1\sqrt{x}\,dx[/imath] since this works out to 0.
What I would do is to sketch the graph for a smaller case, like the sum from 1 to 4, and think about what integral would correspond to the Riemann sum.hm...I need to review my Riemann Sum definition and give this some thought.
Yes, it is clear from the smaller case.What I would do is to sketch the graph for a smaller case, like the sum from 1 to 4, and think about what integral would correspond to the Riemann sum.
Of course, I should know this.The other issue I hinted at is that there is not really one Riemann sum, but many. You could use a left Riemann sum, or a right Riemann sum, or others, and you'd get a slightly different estimate in each case. So the phrase "the Riemann sum" in the hint is misleading; but "use an integral" in the problem itself is appropriate!