# Typical A Level Calculus problem

A curve is given by \(y=x{ e }^{ { -x }^{ 2 } }\).

a) Find the stationary points of the curve and determine their nature.

b) Sketch the curve.

c) Determine the entire area under the curve; given the rule: \[A_{Total}=\int _{ -\infty }^{ \infty }{f(x)} dx\equiv \lim _{ \alpha \rightarrow -\infty }{ \int _{ \alpha }^{ 0 }{f(x)} dx } +\lim _{ \beta \rightarrow \infty }{ \int _{ 0 }^{ \beta }{ f(x) } dx } \]

Submit \(A_{Total}\) as your answer.