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What is the integral of 1 x? - Mathematics Stack Exchange $\begingroup$ "Answers to the question of the integral of 1x are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers" --- not completely correct: if they are both negative it also works This is an improper integral and does not converge in the remaining cases $\endgroup$ –
What is an integral number? - Mathematics Stack Exchange In normal use, integral length would be equal to some integer, while unit length would be of length $1$ (see "unit number" here) Presumably the author meant, "in the unit ( with a different meaning! ) we use to measure lengths, these lengths are integer-valued"
calculus - Is there really no way to integrate $e^{-x^2 . . . $\begingroup$ @user599310, I am going to attempt some pseudo math to show it: $$ I^2 = \int e^-x^2 dx \times \int e^-x^2 dx = Area \times Area = Area^2$$ We can replace one x, with a dummy variable, move the dummy copy into the first integral to get a double integral
What does it mean for an integral to be convergent? The improper integral $\int_a^\infty f(x) \, dx$ is called convergent if the corresponding limit exists and divergent if the limit does not exist While I can understand this intuitively, I have an issue with saying that the mathematical object we defined as improper integrals is "convergent" or "divergent"
How to calculate the integral in normal distribution? It goes without saying that if you're trying to find a CDF, you need to add limits and evaluate the definite integral In the second equation you'll notice that I used "a" as the (upper) limit variable And the question is talking about the CDF, so the lower limit is negative infinity $\endgroup$ –
Bessel Function Integral Identity - Mathematics Stack Exchange The above integral is what you should arrive at when you take the Inversion Integral and integrate over the complex plane Having tested its values for x and t, it appears to be consistent with my result
What does the dx mean in an integral? [duplicate] The $\Sigma$ sign is a sigma and stands for "sum" In an integral you take the limit as $\delta x$ goes to zero So we replace the sigma with another type of s: $\int$ And the $\delta$ gets changed to a d So it is now written: $\int f(x) dx $ and it is the "integral of f(x) with respect to x" But the dx doesn't mean anything on it's own
What is the difference between an indefinite integral and an . . . i think that indefinite integral and anti derivative are very much closely related things but definitely equal to each other indefinite integral denoted by the symbol"∫" is the family of all the anti derivatives of the integrand f(x) and anti derivative is the many possible answers which may be evaluated from the indefinite integral e g
integration - Differentiating Definite Integral - Mathematics Stack . . . For a definite integral with a variable upper limit of integration $\int_a^xf(t)\,dt$, you have ${d\over dx} \int_a^xf(t)\,dt=f(x)$ For an integral of the form $$\tag{1}\int_a^{g(x)} f(t)\,dt,$$ you would find the derivative using the chain rule As stated above, the basic differentiation rule for integrals is: