Question

When creating a left-endpoint Riemann sum on the interval [-29.8, 388.8] using 26 rectangles, the 7th endpoint used to calculate the height of the approximating rectangle would be? Calculate the following showing all your steps.

Answer 1

Suppose that we have a function $f(x)$ on the interval $[-29.8,388.8]$. At first, we divide the interval into $26$ equal parts. We receive the following points:

$\begin{array}{l} -29.8&-13.7&2.4&18.5&34.6&50.7&66.8&82.9&99&115.\\131.2 &147.3&163.4&179.5&195.6&211.7&227.8&243.9&260&276.1\\292.2&308.3&324.4& 340.5&356.6&372.7&388.8 \end{array}$

The 7th endpoint is $66.8$. The left-endpoint Riemann sum has the form: $S=\sum_{i=0}^{25}f(x_i)(x_{i+1}-x_i)$,

where the values $x_i$ are taken from the table.