3. (a) \(\quad y = 5 ^ { x } + \log _ { 2 } ( x + 1 ) , \quad 0 \leqslant x \leqslant 2\)
Complete the table below, by giving the value of \(y\) when \(x = 1\)
| \(x\) | 0 | 0.5 | 1 | 1.5 | 2 |
| \(y\) | 1 | 2.821 | | 12.502 | 26.585 |
(b) Use the trapezium rule, with all the values of \(y\) from the completed table, to find an approximate value for
$$\int _ { 0 } ^ { 2 } \left( 5 ^ { x } + \log _ { 2 } ( x + 1 ) \right) \mathrm { d } x$$
giving your answer to 2 decimal places.
(c) Use your answer to part (b) to find an approximate value for
$$\int _ { 0 } ^ { 2 } \left( 5 + 5 ^ { x } + \log _ { 2 } ( x + 1 ) \right) d x$$
giving your answer to 2 decimal places.