Here's a hint for the height:

If the farthest on the x-axis (horizontally) you can go is 4, then would it not be correct that the farthest on the y-axis (vertically) you can go is y= ?

But, if the tank is full when the work begins, then the distance is only a distance (starting at x=4) from the maximum height. So what do you think the height is?

And as a result, what does your work integral look like?