Question: If \(\vec{F}\left( x,y \right)=\left( 3{{x}^{2}}y,2x-y \right)\), find

\[\int\limits_{\gamma }{\vec{F}\left( \mathbf{x} \right)d\mathbf{x}}\]

where \(\gamma \) is the directed path from (0, 0) to (1, 1) along the graph of the vector equation

\[\mathbf{x}=\left( \sin t,\frac{2t}{\pi } \right)\]

for \(t\in \left[ 0,\frac{\pi }{2} \right]\).