1 thought on “x.e^(-x^2/y)dydx having limits from 0tox for y and 0toinfinite for X.”
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 .
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 .