El cálculo infinitesimal es una herramienta científica y tecnológica de primer nivel, sin duda la más potente y eficaz para el estudio de la naturaleza que hayan desarrollado los matemáticos. Se ...
En Alemania, un genio, robusto, de gran altura y de buen carácter, con apenas tres años menos que Newton, había logrado en el año 1676 concebir el mismo cálculo y lo hizo público inmediatamente, sin ...
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 such as $\frac {x^3} {3} +C$. However, the indefinite integral from $ (-\infty,\infty)$ does exist and it is $\sqrt {\pi}$ so explicitly: $$\int^ {\infty}_ {-\infty} e^ {-x^2} = \sqrt {\pi}$$ Note ...
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 find the area under a curve. I think of them as finding a weighted, total displacement along a curve.
5 An integral domain is a ring with no zero divisors, i.e. $\rm\ xy = 0\ \Rightarrow\ x=0\ \ or\ \ y=0:.:$ Additionally it is a widespread convention to disallow as a domain the trivial one-element ring (or, equivalently, the ring with $: 1 = 0:$). It is the nonexistence of zero-divisors that is the important hypothesis in the definition.
The integral of 0 is C, because the derivative of C is zero. Also, it makes sense logically if you recall the fact that the derivative of the function is the function's slope, because any function f (x)=C will have a slope of zero at point on the function.