# Area by Integration

**Problem**

Divide the circle of radius 13 cm into four parts by two perpendicular chords, both 5 cm from the center. What is the area of the smallest part.

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## 03 Area Enclosed by Cardioids: r = a(1 + sin θ); r = a(1 - sin θ), r = a(1 + cos θ), r = a(1 - cos θ)

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## 08 Area Enclosed by r = a sin 3θ and r = a cos 3θ

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## 05 Area Enclosed by r = a sin 2θ and r = a cos 2θ

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## 01 Area Enclosed by r = 2a cos^2 θ

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## 07 Area Enclosed by r = 2a cos θ and r = 2a sin θ

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## Example 8 | Area bounded by arcs of quarter circles

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## Area for grazing by the goat tied to a silo

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## Cycloid: equation, length of arc, area

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## 709 Centroid of the area bounded by one arc of sine curve and the x-axis

**Problem 709**

Locate the centroid of the area bounded by the x-axis and the sine curve $y = a \sin \dfrac{\pi x}{L}$ from x = 0 to x = L.

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