Right Riemann sum for f(x) = e^x on [0,2] with n = 4

Since $a=0$, $b=2$, and $n=4$, the width of each subinterval is $\Delta x = \frac{2-0}{4} = 0.5$. The subintervals are $[0,0.5], [0.5,1], [1,1.5], [1.5,2]$, so the right endpoints are $x_1 = 0.5$, $x_2 = 1$, $x_3 = 1.5$, and $x_4 = 2$.

The right Riemann sum is $R_4 = \Delta x \left[f(0.5) + f(1) + f(1.5) + f(2)\right] = 0.5\left[e^{0.5} + e^{1} + e^{1.5} + e^{2}\right]$. Evaluating, $e^{0.5} \approx 1.6487$, $e^{1} \approx 2.7183$, $e^{1.5} \approx 4.4817$, and $e^{2} \approx 7.3891$, so $R_4 \approx 0.5(16.2378) \approx 8.1189$.