A force

F $=(3$x$+5$y$),$

where

F

is in newtons and x and y are in meters, acts on an object as the object moves in the x$-$direction from the origin to

x $=4\mathrm{.}79$ m$.$

Find the work

W $=$

F $$ dr

done by the force on the object $($in J$).$

J

$($b$)$

What If$?$ Find the work

W $=$

F $$ dr

done by the force on the object $($in J$)$ if it moves from the origin to $(4\mathrm{.}79$ m$,4\mathrm{.}79$ m$)$ along a straight$-$line path making an angle of $45\mathrm{.}0$ with the positive x$-$axis.

J

Is the work done by this force dependent on the path taken between the initial and final points?

dependentindependent$$