Question 5 - A-Level Maths

Use the trapezium rule with four ordinates (three strips) to find an approximate value for \(\int _ { 2 } ^ { 11 } \sqrt { x ^ { 2 } + 9 } \mathrm {~d} x\). Give your answer to one decimal place.
Describe the geometrical transformation that maps the graph of \(y = \sqrt { x ^ { 2 } + 9 }\) onto the graph of :
1. \(y = 5 + \sqrt { x ^ { 2 } + 9 }\);
2. \(y = 3 \sqrt { x ^ { 2 } + 1 }\).