$($i$)$ Integrate, with respect to $s,$ along the line $($in the $x-y$ plane$)$ which joins the points $A(2,3)$&$B(4,7),$ the function $z=f(x,y),$ where:

$f(x,y)=x^2+xy$

$($ii$)$ Repeat the integration, but this time integrate with respect to $y.$

$[3]$

$($iii$)$ Explain the physical $($geometrical$)$ meaning of these integrals.

$[1]$