3.
$$y = \sqrt { \left( 3 ^ { x } + x \right) }$$
- Complete the table below, giving the values of \(y\) to 3 decimal places.
| \(x\) | 0 | 0.25 | 0.5 | 0.75 | 1 |
| \(y\) | 1 | 1.251 | | | 2 |
- Use the trapezium rule with all the values of \(y\) from your table to find an approximation for the value of
$$\int _ { 0 } ^ { 1 } \sqrt { \left( 3 ^ { x } + x \right) } \mathrm { d } x$$
You must show clearly how you obtained your answer.
- Explain how the trapezium rule could be used to obtain a more accurate estimate for the value of
$$\int _ { 0 } ^ { 1 } \sqrt { \left( 3 ^ { x } + x \right) } d x$$
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