I have to prove that the value of $$\int_0^{\infty}ae^{-ax^2}dx$$ does not depend on $a>0$. I have thought to show the convergence of the integral but then how can I conclude this resul does not depend on $a$?
2026-04-01 07:17:23.1775027843
Show value of $\int_0^{\infty}ae^{-a\cdot x^2}dx$ is independent on $a$
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In your integral make the substitution $y=\frac{x}{a}$. This gives $$\int_0^{\infty}e^{-x^2}dx$$ a definite integral which does not involve $a$.
NOTE This answer was for the question as originally set. The OP has now changed the question into a form where the result is incorrect.