Use sums of the form ∑ 𝑓(𝑥𝑖) 𝛿𝑥𝑖𝑖 to estimate the area under the curve 𝑦 = 𝑓(𝑥).

The diagram shows the graph of $y = g(x)$ from $x = 0$ to $x = 5$. Calculate the estimate of the area under the curve using the sum $\sum_{i=1}^{5} g(x_i)\delta x_i$ with $x_1 = 1$, $x_2 = 2$, $x_3 = 3$, $x_4 = 4$, $x_5 = 5$ and $\delta x_i = 1$ for all $i$.

A student uses four rectangles of equal width to estimate the area under the curve \( y = f(x) \) between \( x = 2 \) and \( x = 6 \), using the left endpoint of each subinterval. The diagram below shows the curve and the four rectangles. The left endpoints used are \( x = 2, 3, 4, 5 \) with corresponding function values \( f(2) = 8.5 \), \( f(3) = 7.2 \), \( f(4) = 5.8 \), \( f(5) = 4.3 \). The estimate of the area is

The graph shows the function $g(x) = 6 - 0.2x^2$ on the domain $0 \leq x \leq 5$. Use a right-endpoint Riemann sum with five equal subintervals to estimate the area under the curve between $x = 0$ and $x = 5$.

The graph shows the function $g(x) = 6 - 0.2x^2$ on the interval $[0, 5]$. Using five rectangles of equal width with right endpoints at $x = 1, 2, 3, 4, 5$, calculate the area estimate given by $\sum_{i=1}^{5} g(x_i)\delta x_i$.