Last updated on Oct 23, 2026

Parametric Integration (AQA A-Level Mathematics): Flashcards

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Parametric Integration

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Formula for area under parametric curve

$\int y \, dx$

Converting $dx$ to $dt$ in parametric integration

Find $\frac{dx}{dt}$ , then $dx = \frac{dx}{dt} \, dt$

When converting to parameter $t$ , what must also change?

Limits of integration

$\frac{dx}{dt}$ when $x = 1 + t$

$1$

$t$ value when $x=2$ (given $x=1+t$ )

$t=1$

$t$ value when $x=6$ (given $x=1+t$ )

$t=5$

Evaluate: $\int_{1}^{5} (1 - \frac{1}{t}) \, dt$

$[t - \ln|t|]_{1}^{5} = 4 - \ln 5$

$\frac{dx}{dt}$ when $x = 3t$

$3$

Values of $t$ where $\sin(t)=0$ (first period)

$t=0$ and $t=\pi$

Evaluate: $\int_{0}^{\pi} 3\sin(t) \, dt$

$[-3\cos(t)]_{0}^{\pi} = 6$

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Parametric Equations

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Parametric Equations

Further Parametric Equations

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