$($a$)$

A force

F $=(3$x$+4$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 $=5\mathrm{.}21$ 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 $(5\mathrm{.}21$ m$,5\mathrm{.}21$ m$)$ along a straight$-$line path making an angle of $45\mathrm{.}0$ with the positive x$-$axis.

J