- #1
metrictensor
- 117
- 1
Does anyone know how to go about solving
[itex]\int e^{(x^{2})} dx[/itex]
[itex]\int e^{(x^{2})} dx[/itex]
This is helpful. I have the bounds. Thaks. It is weird that there is no analytical solution to something that looks so simple. I did write a taylor series and integrated that to get an infinite sum that is equal to the integral. It is:Data said:not expressible in terms of elementary functions. Using the "special" function, [itex]\mbox{erf} (x)[/itex] (the "error function", defined by [itex]\mbox{erf}(x) = 2/\sqrt{\pi} \int_0^x e^{-t^2} \ dt[/itex]), you can express the integral in this way, though:
[tex]\int e^{(x^2)} \ dx = -\frac{i\sqrt{\pi}}{2}\mbox{erf}(ix)+C.[/tex]
Essentially what this means is that you either have to compute definite integrals with this integrand numerically, or look up values on tables for the error function.
An integral is a mathematical concept that represents the area under a curve in a graph. It is used to solve problems involving continuous functions and is an important tool in calculus.
To evaluate an integral, you can use different techniques such as substitution, integration by parts, and trigonometric substitution. You can also use tables, graphs, and numerical methods to approximate the value of an integral.
Evaluating an integral allows us to find the exact value of the area under a curve, which can be useful in many real-world applications. It also helps in solving problems related to velocity, acceleration, and other physical quantities.
The two main types of integrals are indefinite and definite integrals. Indefinite integrals do not have limits of integration and result in a function, while definite integrals have specific limits of integration and result in a numerical value.
The fundamental theorem of calculus states that the derivative of an integral is equal to the original function. This means that integrals and derivatives are inverse operations of each other, and they are closely related in calculus.