1.
$$y = \sqrt { \left( 2 ^ { x } + x \right) }$$
a. Complete the table below, giving the values of \(y\) to 3 decimal places.
| \(x\) | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1 |
| \(y\) | 1 | 1.161 | 1.311 | | | 1.732 |
(1)
b. Use the trapezium rule with all the values of \(y\) from your table to find an approximation for the value of
$$\int _ { 0 } ^ { 1 } \sqrt { \left( 2 ^ { x } + x \right) } \mathrm { d } x$$
giving your answer to 3 significant figures.
Using your answer to part (b) and making your method clear, estimate
c. \(\int _ { 0 } ^ { 0.5 } \sqrt { \left( 2 ^ { 2 x } + 2 x \right) } \mathrm { d } x\)