Overview (Leaving Cert Applied Maths): Flashcards

$\frac{x^{n+1}}{n+1} + c$

$\ln x + c$

$\frac{1}{a}\ln(ax + b) + c$

$\int_a^b f(x)dx = F(b) - F(a)$

$\int u \, dv = uv - \int v \, du$

Choosing $u$ in integration by parts

$v = \frac{ds}{dt}$ (first derivative of distance)

$a = \frac{dv}{dt}$ (first derivative of velocity)

$W = \int_a^b F(x)dx$

Arbitrary constants

Initial conditions to find specific constants

$\frac{dy}{dx}$, then $\frac{d^2y}{dx^2} = v\frac{dv}{dy}$

Differentiation of constant gives zero