Parametric, Polar & Vectors formula sheet

12 rows · CalcRef · sample of the first 6 rows

Parametric, Polar & Vectors
Formula	Statement	Conditions
Parametric Derivative (dy/dx)	$\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{y'(t)}{x'(t)}$	x'(t) ≠ 0.
Parametric Arc Length	$L = \int_\alpha^\beta \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2}\, dt$	no restriction stated
Parametric Area	$A = \int_\alpha^\beta y(t)\, x'(t)\, dt$	no restriction stated
Polar to Cartesian	$x = r\cos\theta, \quad y = r\sin\theta, \quad r^2 = x^2 + y^2, \quad \tan\theta = y/x$	no restriction stated
Polar Area	$A = \frac{1}{2}\int_\alpha^\beta [r(\theta)]^2 \, d\theta$	no restriction stated
Polar Arc Length	$L = \int_\alpha^\beta \sqrt{r^2 + \left(\frac{dr}{d\theta}\right)^2}\, d\theta$	no restriction stated

The 12 Parametric, Polar & Vectors formulas in the CalcRef library, every one of them free to read at /topics/parametric-polar-vectors.

CalcRef is an educational reference. Check every statement on this sheet against your own course notes, textbook or exam formula policy before relying on it in graded work.

Every formula on this sheet is also free on its own page — browse the full reference. Premium pays for the sheet, not the mathematics.