4 A spreadsheet is used to approximate \(\int _ { a } ^ { b } f ( x ) d x\) using the midpoint rule with 1 strip. The output is shown in the table below.
| B | C | D |
| 3 | \(x\) | \(\mathrm { f } ( x )\) | \(\mathrm { M } _ { 1 }\) |
| 4 | 1.5 | 1.3103707 | 0.65518535 |
The formula in cell C4 is \(= \mathrm { B } 4 \wedge ( 1 / \mathrm { B } 4 )\).
The formula in cell D4 is \(= 0.5 ^ { * } \mathrm { C } 4\).
- Write the integral in standard mathematical notation.
A graph of \(y = f ( x )\) is included in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{4023e87c-34b1-4abd-9acc-ede5e4d68c7f-04_789_1004_1199_235} - Explain whether 0.65518535 is an over-estimate or an under-estimate of \(\int _ { a } ^ { b } f ( x ) d x\).