Calculus & Differential Equations (Leaving Cert Applied Maths): Flashcards

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

Differentiation of constant gives zero

$\ln x + c$

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

Exact area between curve and x-axis over interval

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

Choose $u$ in integration by parts

$v = \frac{ds}{dt}$

$a = \frac{dv}{dt}$

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

Separate variables, then integrate both sides

Particular uses initial conditions to find constant

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

$P = kQ$ where $k$ is constant of proportionality

Choose $u$, find $dx$ in terms of $du$, substitute, solve, back-sub