In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Find the first three terms, in ascending powers of \(x\), of the binomial expansion of
$$( 3 + x ) ^ { - 2 }$$
writing each term in simplest form.
Using the answer to part (a) and using algebraic integration, estimate the value of
$$\int _ { 0.2 } ^ { 0.4 } \frac { 6 x } { ( 3 + x ) ^ { 2 } } d x$$
giving your answer to 4 significant figures.
Find, using algebraic integration, the exact value of
$$\int _ { 0.2 } ^ { 0.4 } \frac { 6 x } { ( 3 + x ) ^ { 2 } } d x$$
giving your answer in the form \(a \ln b + c\), where \(a , b\) and \(c\) are constants to be found.