Question

Express the integral as a limit of riemann sums. do not evaluate the limit. 5 (sqrt(6 + x^2)) dx 3

Answer 1

$\displaystyle \int\limits^5_3 {x\sqrt{6+x^2}} \, dx = \lim_{n \to \infty} \sum\limits_{k=0}^{n-1}\left(\frac{5-3}{n}\sqrt{6+\left(\frac{k(5-3)}{n}+3\right)^{2}}\right)$