Question

I'm supposed to write the following as a definite integral and evaluate it, can someone check it for me?

Answer 1

\( \lim_{x \rightarrow \infty} \displaystyle\sum\limits_{k=1}^n (\sqrt{(1+\frac{3k}{n})}\cdot\frac{3}{n}) \)

My answer:
\(\int_{1}^{4}\sqrt{x}dx = \frac{14}{3}\)

Answer 2

looks good.

Answer 3

"n --> infinity"
typo..

Answer 4

Thanks for the confirmation (: