Limit of a Riemann Sum as $n$ approaches to infinity of $f(t)=150t^{0.5}$

Asked Dec 21 '21 at 04:16

Active May 29 '22 at 17:28

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I got a function which is $f(t)=150t^{0.5}$. I need is to find the limit of a Riemann sum as $n$ approaches to infinity.

$\Large\int_0^9150t^{0.5}dt = \lim \limits_{n \to \infty}\sum_{i=1}^nf\bigg(0+i\frac9n\bigg)$

Solving Further
$= \lim \limits_{n \to \infty}\frac9n\sum_{i=1}^nf\Big(i\frac9n\Big) \\ = \lim \limits_{n \to \infty}\frac9n\sum_{i=1}^n150\Big(\frac{9i}n\Big)^{0.5} $

And I'm stuck in this step and don't know what to do next. Can someone help me?

edited May 29 '22 at 17:28

Rohit Singh

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asked Dec 21 '21 at 04:16

Newbie104

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For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – Wolgwang Dec 21 '21 at 04:19
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You should type out the question instead of posting the image so that it can be searched by search engines. – Wolgwang Dec 21 '21 at 04:20
If this does not meet your needs, pick a nonuniform partition so you are not summing $\sqrt{i}$. (The $150 \sqrt{\frac{9}{n}}$ are constants when appearing in a sum with index $i$, so can be (un-)distributed from the sum to a coefficient of the sum.) – Eric Towers Dec 21 '21 at 04:28

Limit of a Riemann Sum as $n$ approaches to infinity of $f(t)=150t^{0.5}$

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