Find the formula for the Riemann sum obtained by dividing the interval [3,4]\displaystyle {\left[{3},{4}\right]} into n\displaystyle {n} equal subintervals and using the right endpoint for each ck\displaystyle {c}_{{k}}. Then take the limit of these sums as n\displaystyle {n}\to\infty to calculate the area under the curve f(x)=8x\displaystyle {f{{\left({x}\right)}}}={8}{x} over [3,4]\displaystyle {\left[{3},{4}\right]}.

The area under the curve over [3,4]\displaystyle {\left[{3},{4}\right]} is square units.