So the question is: A curve rise from the origin of the xy plane into the 1st quadrant. The area under the curve from (0,0) to (x,y) is 1/5 the area of the rectangle with these points as opposite vertices.

So i'm solving for f(x):

So far what i have is:

Area(D)=1/5 xy=integral 0 to x y(t)dt

and then

rewrite as: 1/5xy = integral 0 to x g(x-t)y(t) dt, where g(t)=1

then the next step i get stuck, because when i take the Laplace of both sides i get: 1/5L[xy]=L[y]

Thanks in advance for any help.