Answer
$\lim\limits_{n \to {\infty}}\Sigma_{i=1}^{n}{\sqrt {4+\left(1+\frac{2i}{n}\right)^2}}\frac{2}{n}$
Work Step by Step
$f(x)$ = $\sqrt {4+x^{2}}$
$a$ = $1$, $b$ = $3$ and $Δx$ = $\frac{3-1}{n}$ = $\frac{2}{n}$
$x_i$ = $1+i$
$Δx$ = $\frac{2}{n}$, $x = 1+\frac{2i}{n}$
so
$\int_1^3{\sqrt {4+x^{2}}}dx$ = $\lim\limits_{n \to {\infty}}\Sigma_{i=1}^{n}{\sqrt {4+\left(1+\frac{2i}{n}\right)^2}}\frac{2}{n}$
