Integrate e^(-x^2/2) dx
What branch of calculus is this? Is this differential equations?
Nope, just and ordinary integral. However, it is a special integral, called the error function. Look that up.
That's what I needed. Thanks so much for the help!
To integrate the function e^(-x^2/2) dx, you need to use techniques from integral calculus. Specifically, this is an example of an indefinite integral, where the goal is to find the antiderivative of a function.
This problem does not specifically relate to differential equations. Differential equations study the relationship between a function and its derivatives. On the other hand, this question involves finding the integral of a given function.
To solve this specific integral, there is no elementary function that can represent its antiderivative. However, the integral does have a well-known special function associated with it—the Gaussian integral.
The Gaussian integral is defined as:
∫ e^(-x^2) dx
By manipulating the original integral, you can obtain the Gaussian integral:
∫ e^(-x^2/2) dx = √(2π) ∫ e^(-x^2) dx
The value of the Gaussian integral is √(π), making the integral of e^(-x^2/2) dx equal to √(2π). This result can be found using advanced techniques such as contour integration or by using tables of special integrals.
In summary, the integration of e^(-x^2/2) dx falls under integral calculus, but it is not directly related to differential equations. The result is √(2π), making use of the Gaussian integral.