6 Fig. 6 shows a partially completed spreadsheet.
This spreadsheet uses the trapezium rule with four strips to estimate \(\int _ { 0 } ^ { \frac { 1 } { 2 } \pi } \sqrt { 1 + \sin x } \mathrm {~d} x\).
\begin{table}[h]
| A | B | C | D | E |
| 1 | | \(x\) | \(\sin x\) | \(y\) | |
| 2 | 0 | 0.0000 | 0.0000 | 1.0000 | 0.5000 |
| 3 | 0.125 | 0.3927 | 0.3827 | 1.1759 | 1.1759 |
| 4 | 0.25 | 0.7854 | 0.7071 | 1.3066 | 1.3066 |
| 5 | 0.375 | 1.1781 | 0.9239 | 1.3870 | 1.3870 |
| 6 | 0.5 | 1.5708 | 1.0000 | 1.4142 | 0.7071 |
| 7 | | | | | 5.0766 |
| 8 | | | | | |
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{table}
- Show how the value in cell B3 is calculated.
- Show how the values in cells D2 to D6 are used to calculate the value in cell E7.
- Complete the calculation to estimate \(\int _ { 0 } ^ { \frac { 1 } { 2 } \pi } \sqrt { 1 + \sin x } \mathrm {~d} x\).
Give your answer to 3 significant figures.