Integrating Into Integration

Don’t we love our integration slang.

[!Note] Some of this I use with my maths friends, some I use personally. Most of them aren’t widely established or accepted mathematical terms, but… you could help spread them ;)

catalyst

You’re looking for a catalyst here.

Multiplying through (or dividing by) a factor when integrating a fraction. Reference to Integration is Like Organic Chemistry.

evolution

You probably only want one of primitives or evolutions.

Refers to $\tan$ and $\sec$ , which are ‘evolutions’ of the primitive trigonometric functions:

an{x} = rac{sin{x}}{cos{x}} qquad sec{x} = rac{1}{cos{x}}

Notes

$\cot$ and $\csc$ are also evolutions, ofc, but they feel a bit more ‘outlandish’.

We pair the trigonometric functions in this way because their derivatives match up nicely:

egin{align*} rac{d}{dx} sin{x} &= cos{x} qquad cos{x} = -sin{x} \ rac{d}{dx} an{x} &= sec^2{x} qquad sec{x} = sec{x} an{x} end{align*}

famously

e^x is famously both the derivative and antiderivative of e^x.

Well-known, well-established.

primitive

Try reducing to primitives.

Refers to $\sin$ and $\cos$ , the ‘primitive’ trigonometric functions. Can also be extended to mean $\sinh$ and $\cosh$ in a hyperbolic context.

See also evolution, which refers to $\tan$ and $\sec$ .

quotable

It’s quotable from here.

A solution is quotable if it’s sufficiently simple to jump straight to the answer, i.e. “quote” it. It can also refer to “quoting” a formula from a formula book.

straight-up layer cake

That’s straight-up layer cake mate.

Refers specifically to integrating a fraction where the numerator is the derivative of the denominator, in which case

int rac{f'(x)}{f(x)} dx = lnleft| f(x) ight| + c