The following sum
$$ \sqrt{49-\frac{7}{n}^2}\cdot\frac{7}{n} + \sqrt{49-\frac{14}{n}^2}\cdot\frac{7}{n} + \cdots
+ \sqrt{49-\frac{7n}{n}^2}\cdot\frac{7}{n} $$
is a right Riemann sum for the definite integral
$$ \int_0^b f(x)\,dx
$$
Find $b, f(x)$ and the limit of these Riemann sums as $n \to \infty$.
Best Answer
The integral is: $\displaystyle \int_{0}^7 \sqrt{49 - x^2} dx$. It appears that your Riemann sum is mistyped because you missed an $n$ at the denominator and it is supposed to be $n^2$.