1 It is given that \(y = \sinh \left( x ^ { 2 } \right) + \cosh \left( x ^ { 2 } \right)\).
- Use standard results from the list of formulae (MF19) to find the Maclaurin's series for \(y\) in terms of \(x\) up to and including the term in \(x ^ { 4 }\).
- Deduce the value of \(\frac { \mathrm { d } ^ { 4 } \mathrm { y } } { \mathrm { dx } ^ { 4 } }\) when \(x = 0\).
- Use your answer to part (a) to find an approximation to \(\int _ { 0 } ^ { \frac { 1 } { 2 } } \mathrm { ydx }\), giving your answer as a rational
fraction in its lowest terms. fraction in its lowest terms.