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The area of a circle of radius R is A = pi*R², derivable by choosing an elemental area and integrating. Using which of the following elemental shapes can the area be correctly obtained by integration?

1. A thin ring concentric with the circle.
2. A thin almost-rectangular strip at a distance less than R from the centre.
3. A thin sector of the circle.
4. All of these elemental shapes work.

Correct answer: All of these elemental shapes work.

Solution

Each elemental shape can sweep the entire disc with a single integration variable and each integrates to pi*R², so all three are valid.

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