The rectangles in the graph below illustrate a left endpoint Riemann sum for $$ f(x)=\frac{x^{2}}{10} $$ on the interval $$ [3,7] $$. The value of this left endpoint Riemann sum is 8.6 Riemann sum is an underestimate of $$ \rightarrow $$ the area of the region enclosed by $$ y=f(x) $$, the x -axis, and the vertical lines $$ \mathrm{x}=3 $$ and $$ \mathrm{x}=7 $$.

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To find the left endpoint Riemann sum for the function $$ f(x) = \frac{x^2}{10} $$ on the interval $$ [3,7] $$, we need to divide the interval into subintervals and calculate the area of each rectangle.

Given that the value of the left endpoint Riemann sum is 8.6, we can set up the equation:

$$ \text{Left Endpoint Riemann Sum} = \sum_{i=1}^{n} f(x_i) \Delta x $$

where:
- $$ f(x_i) $$ is the function value at the left endpoint of each subinterval,
- $$ \Delta x $$ is the width of each subinterval.

Since the function is $$ f(x) = \frac{x^2}{10} $$ and the interval is $$ [3,7] $$, we can calculate the left endpoint Riemann sum by dividing the interval into subintervals and calculating the area of each rectangle.

Let's calculate the left endpoint Riemann sum for the function $$ f(x) = \frac{x^2}{10} $$ on the interval $$ [3,7] $$ and then determine the area of the region enclosed by $$ y=f(x) $$, the x-axis, and the vertical lines $$ x=3 $$ and $$ x=7 $$.
The left endpoint Riemann sum for $$ f(x) = \frac{x^2}{10} $$ on the interval $$ [3,7] $$ is 8.6. This sum is an underestimate of the area under the curve $$ y=f(x) $$ between $$ x=3 $$ and $$ x=7 $$.

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