Use the right-endpoint approximation $$\style{font-size:18pt…

Use the right-endpoint approximation $$\style{font-size:18pt}{R_n}$$ to find an 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 $$\style{font-size:18pt}{n\rightarrow \infty.}$$The following formulae may be useful:$$\style{font-size:18pt}{\sum_{i=1}^{n} 1  = 1+ 1 + 1+ \dots + 1 = n,}$$$$\style{font-size:18pt}{\sum_{i=1}^{n} i = 1+ 2 + 3+ \dots + n = \dfrac{n(n+1)}{2},}$$$$\style{font-size:18pt}{\sum_{i=1}^{n} i^2  = 1^2+2^2+3^2+\dots+n^2 = \dfrac{n(n+1)(2n+1)}{6}.}$$