Differential and integral proportional calculus: how to find a primitive for f(x)=1/2πe−(1/2)x2

Abstract

We present a type of arithmetic called Proportional Arithmetic. The main properties and objects that emerge with this way of operating quantities are exposed. Finally, the antiderivative and the indefinite integral are defined in order to calculate the primitive of $f\left(x\right)=1/\sqrt{2\pi }{e}^{-\left(1/2\right)x^2}$ in the Proportional context.

Keywords:

• Proportional arithmetic
• calculus
• teaching differential and integral calculus

2010 Mathematics Subject Classifications:

• 26A15
• 26A24
• 26A42
• 34A24
• 34A30

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Note that in this arithmetic 0 represents $-\mathrm{\infty }$. (Think in the homeomorphism $f\left(x\right)=\ln \left(x\right)$.)

Additional information

Funding

This work was supported by FONDECYT [1120709 and 1170466] and DIUDA scientific initiation [22372].