Question

x.e^(-x^2/y)dydx having limits from 0tox for y and 0toinfinite for X.​

Answer 1

Step-by-step explanation:

Well this DOES look like a job for a simple u-sub and after this a limit question, which i freely admit am not the guy for. Anyway let's try.

∫xe−x2dx .

Let x2=u , and taking the derivative of both sides gives dudx=2x , meaning that dx=du2x .

∫12e−udu=−12eu .

Substituting this back, we get ∫xe−x2dx=−12ex2 .

That was the easy part. Now we need to evaluate the boundaries of integration and subtract. I'll start with the lower bound as 0 is the easier of the two as e0=1 , so −12e0=−12 .

limx→∞12ex2=0 .

0−−12=12 .

So the integral from 0 to ∞ is 12 .