Exercise · ZW-POLAR-COORDINATES-004 · ★☆☆ Basic
Using \(dA=r\,dr\,d\theta\), compute the area of the disc of radius \(2\): \(\int_0^{2\pi}\!\int_0^2 r\,dr\,d\theta\).
Choose one option.
Show answer
- B. \(4\pi\)
Explanation
\(\int_0^2 r\,dr=2\) and \(\int_0^{2\pi}2\,d\theta=4\pi\), which matches \(\pi R^2\) for \(R=2\).
Review the concept: Polar coordinates
Polar coordinates locate a point of the plane by its distance \(r\) from the origin and the angle \(\theta\) its radius makes with the positive \(x\)-axis.
\[x=r\cos\theta,\quad y=r\sin\theta\]
More practice problems: polar coordinates
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