Laplace Question

Limits, differentiation, related rates, integration, trig integrals, etc.
acer400
Posts: 2
Joined: Thu Dec 15, 2011 5:44 pm
Contact:

Laplace Question

Postby acer400 » Thu Dec 15, 2011 5:50 pm

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.

nona.m.nona
Posts: 269
Joined: Sun Dec 14, 2008 11:07 pm
Contact:

Re: Laplace Question

Postby nona.m.nona » Fri Dec 16, 2011 1:03 am

Is it necessary to use Laplace transforms, rather than any other method?

Thank you.

acer400
Posts: 2
Joined: Thu Dec 15, 2011 5:44 pm
Contact:

Re: Laplace Question

Postby acer400 » Fri Dec 16, 2011 2:01 am

I think i just need to use laplace to get to the current step and solve using ODE after that, but i am unsure if that is correct?

nona.m.nona
Posts: 269
Joined: Sun Dec 14, 2008 11:07 pm
Contact:

Re: Laplace Question

Postby nona.m.nona » Fri Dec 16, 2011 5:12 pm

I could be incorrect, but it seems to me that other methods are available. In very crude terms, perhaps the following is useful:











Return to “Calculus”