The integral of e^(-x^2) from 0 to infinity is convergent, as established through the comparison theorem. By comparing e^(-x^2) to the function e^(-x), which is known to converge, one can demonstrate that e^(-x^2) is bounded above by a convergent integral. This method effectively confirms the convergence of the original integral without needing complex calculations.
PREREQUISITESStudents studying calculus, particularly those focusing on integral convergence, as well as educators seeking to enhance their teaching methods related to the comparison theorem.
spaniks said:Homework Statement
use the comparison theorem to show that the integral of e^(-x^2) from 0 to infinity is convergent.
Homework Equations
None
The Attempt at a Solution
In class we have never dealt with using the comparison theorem with the exponential function so I was not sure what I function I would compare it to in order to solve this problem. Could I compare it to something like e^(-x)?