Parametric Integration (Edexcel A-Level Mathematics): Flashcards

$A = \int y(t) \frac{dx}{dt} dt$, integrating with respect to $t$.

Use $dx/dt$ and multiply by $dt$ to find $dx$.

$dx/dt = 1$.

From $t=1$ to $t=5$.

I = $\int_{1}^{5} (1 - 1/t) dt$.

$I = 4 - \ln(5)$ from the integration process.

$x = 3t$, $y = \sin(t)$.

$t = 0, \pi,$ and $2\pi$.

$dx = 3dt$.

$I = 6$.