Question

For the function, approximate the area under the curve on the specified interval as directed?

`f(x)=x10^x` on `[0,4]` with 4 subintervals of equal width and midpoints for sample points.

Answer 1

Approximately `11,908` square units

Explanation:

4 intervals on `[0,4]` implies strips of width `1` unit and sample points of `{0.5,1.5.2.5.3.5}`
Since each strip is 1 unit in width the approximated area of each strip will be the value of the expression at `x10^x` for each sample point.
Using a spreadsheet to do the actual calculations:

we get an approximation of about `11908`