The work performed against a drag force (2)

The position vector of a particle is given by,

$y$

$x$

Here $t$ is the time in seconds. The particle moves through a viscous fluid and there is a drag force on the particle $\vec{F} =-|\vec{v}|\vec{v}$. How much work is required to move this particle between time $t=0$ seconds and $t=$  seconds?

$W=$  [J]