Use the right-endpоint аpprоximаtiоn $$style{font-size:18pt}{R_n}$$ to find аn approximation to the area under the curve $$style{font-size:18pt}{f(x)=4x}$$ on the interval $$style{font-size:18pt}{[0,3]}$$, and then find the exact area as the limit of the Riemann sum $$style{font-size:18pt}{R_n}$$ as $$style{font-size:18pt}{nrightarrow infty.}$$The following formulae may be useful:$$style{font-size:18pt}{sum_{i=1}^{n} 1 = 1+ 1 + 1+ dots + 1 = n,}$$$$style{font-size:18pt}{sum_{i=1}^{n} i = 1+ 2 + 3+ dots + n = dfrac{n(n+1)}{2},}$$$$style{font-size:18pt}{sum_{i=1}^{n} i^2 = 1^2+2^2+3^2+dots+n^2 = dfrac{n(n+1)(2n+1)}{6}.}$$