Edexcel C2 2017 June — Question 3

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2017
SessionJune
TopicArea Under & Between Curves

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 \(x = 1\)
\(x\)00.511.52
\(y\)12.82112.50226.585
(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.