- #1
z00maffect
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Homework Statement
[tex]\int^{\infty}_{-\infty}(1/(a^{4}+(x-x_{0})^{4}))dx[/tex]
Homework Equations
The Attempt at a Solution
i let [tex]u = (x-x_{0})^{4}[/tex]
but have no idea what to go from there
Last edited:
z00maffect said:awesome thanks! got [tex]\pi*\sqrt{2}/2[/tex]
An infinite limit in integration refers to the upper or lower bound of the integral being either positive or negative infinity. This means that the function being integrated does not have a finite upper or lower bound, and the integral will continue indefinitely.
To handle an infinite limit in integration, you can use a variety of techniques such as substitution, integration by parts, or partial fractions. You may also need to apply certain rules, such as L'Hopital's rule, to evaluate the integral.
Yes, it is possible to evaluate an integral with infinite limits analytically. However, it may require advanced mathematical techniques and may not always result in a closed-form solution.
Integrals with infinite limits have many applications in mathematics, physics, and engineering. For example, they can be used to calculate areas under curves, volumes of shapes, and work done by varying forces.
Yes, there are various strategies for solving integrals with infinite limits, such as using symmetry, manipulating the integrand, and using known integrals as a reference. It is also important to consider the behavior of the function near the infinite limits to determine the convergence of the integral.