Lengths and Surface Areas (AQA A-Level Further Maths): Quizzes

$s = \int_{x_1}^{x_2} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx$

$s = \int_{t_1}^{t_2} \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt$

$S = 2\pi \int_{x_1}^{x_2} y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx$

Surface area has $2\pi y$ factor

Pythagoras' theorem

$1$

Forgetting to square the derivative

$2\pi$ radians

The integration limits

A frustum (truncated cone)