lost_math said:Homework Statement
Integrate the function e^(-x^2) with definite integrals -infinity to X
Integrating the function e^(x^2) allows us to determine the area under the curve of the function, which has many real-world applications in fields such as physics, engineering, and economics.
No, it is not possible to find an exact solution for the integral of e^(x^2) using elementary functions. However, it can be approximated using numerical methods.
The integral of e^(x^2) can be solved using the substitution method, where u = x^2 and du = 2x dx. This results in the integral becoming ∫e^u (du/2), which can then be solved using integration by parts or the power rule.
The integral of e^(x^2) from 0 to infinity is equal to √π/2, which is approximately 1.77245.
Yes, the integral of e^(x^2) is often used as a building block to solve other integrals. It can be used to solve integrals involving other exponentials, trigonometric functions, and more complex functions.