integrals background

integrals

/ˈɪntɪɡrəlz/ /ˈɪntɪɡəlz/

Illustration integrals - Image 1

noun

Integral, Integrale

A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.

Examples :

"The integral of xmapsto x^2 on [0,1] is rac{1}{3}."

Das Integral von xmapsto x^2 auf [0,1] ist 1/3.

math number science technical

Illustration integrals - Image 1

noun

Bestimmtes Integral, Limes von Summen

A definite integral, a limit of sums.

Examples :

"To calculate the total amount of water collected during the rain, we can use integrals to add up the rainfall amounts over very short intervals of time. "

Um die Gesamtmenge des während des Regens gesammelten Wassers zu berechnen, können wir bestimmte Integrale verwenden, um die Niederschlagsmengen über sehr kurze Zeitintervalle zu addieren.

Illustration integrals - Image 1

noun

Stammfunktion

Antiderivative

Examples :

"The integral of x^2 is rac{x^3}{3} plus a constant."

Die Stammfunktion von x^2 ist x^3/3 plus einer Konstanten.