- #1
Vorde
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- 0
Is there any function such that:
[itex]_{-∞}[/itex][itex]\int[/itex][itex]^{∞}[/itex]f(x) dx
Is any integer except 0 and ∞?
[itex]_{-∞}[/itex][itex]\int[/itex][itex]^{∞}[/itex]f(x) dx
Is any integer except 0 and ∞?
Vorde said:Is there any function such that:
[itex]_{-∞}[/itex][itex]\int[/itex][itex]^{∞}[/itex]f(x) dx
Is any integer except 0 and ∞?
Vorde said:I looked it up, apparently is an equation that satisfies the statement that the integral from -∞ to ∞ is 1, but because of the way it's defined it isn't actually a function.
phyzguy said:There are an infinite number of such functions. For example:
[tex]\int^\infty_{-\infty}e^{-x^2}dx = \sqrt{\pi}[/tex]
so if:
[tex]f(x) = \frac{7}{\sqrt\pi}e^{-x^2}[/tex]
then:
[tex]\int^\infty_{-\infty}f(x)dx = 7[/tex]
There are lots of functions like this that one can play this game with.
A general integral question is a mathematical problem that involves finding the antiderivative or the area under a curve of a function. It is a fundamental concept in calculus and is used to solve a variety of real-world problems.
To solve a general integral question, you need to use integration techniques such as substitution, integration by parts, or partial fractions. These methods help to find the antiderivative of the given function, which can then be used to calculate the area under the curve.
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