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What does it mean for an "integral" to be convergent?
The noun phrase "improper integral" written as $$ int_a^infty f (x), dx $$ is well defined. If the appropriate limit exists, we attach the property "convergent" to that expression and use
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Why must the curve of an integral intersect the origin?
The other kind of integral you often encounter is the definite integral. This is the integral that is sometimes described as "the area under the curve" (although I would consider that an
What is the integral of 1/x?
Answers to the question of the integral of $frac {1} {x}$ are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers.
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Various methods for Integral from MIT Integration Bee 2026 Semifinal
Encountering the integral $$ int frac{x^2-2}{left(x^2+2right) sqrt{x^4+4}} d x, $$ from MIT integration 2026 Semifinal, I tried my best to finish it within the time limit. $$
Can the integral closure of a ring be taken intrinsically?
However, one "intrinsic integral closure" that is often used is the normalization, which in the case on an integral domain is the integral closure in its field of fractions. It''s the maximal integral
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solving the integral of $e^ {x^2}$
The integral which you describe has no closed form which is to say that it cannot be expressed in elementary functions. For example, you can express $int x^2 mathrm {d}x$ in elementary functions
What is an integral?
A different type of integral, if you want to call it an integral, is a "path integral". These are actually defined by a "normal" integral (such as a Riemann integral), but path integrals do not seek to
calculus
@user599310, I am going to attempt some pseudo math to show it: $$ 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
calculus
Integral of ln (sin (x)) Ask Question Asked 1 year, 9 months ago Modified 1 year, 9 months ago
Volume of a pyramid, using an integral
Volume of a pyramid, using an integral Ask Question Asked 14 years, 7 months ago Modified 14 years ago
Evaluation of Gaussian integral $int_{0}^{infty} mathrm{e}^{-x^2} dx$
Both formulas can be used for many special integrals like the Fresnel Integral or the Sinc Integral and much more. Note that one could directly derive this result from $Gamma (1/2)$ by
integration
I was reading on Wikipedia in this article about the n-dimensional and functional generalization of the Gaussian integral. In particular, I would like to understand how the following equations are
calculus
Evaluate an integral involving a series and product in the denominator Ask Question Asked 1 month ago Modified 1 month ago