We consider an elemental triangular sector (Figure I.6) between \( \theta \) and \( \theta + \delta \theta \) . The "height" of the triangle is r and the "base" is \( r \delta \theta \). The horizonta...We consider an elemental triangular sector (Figure I.6) between \( \theta \) and \( \theta + \delta \theta \) . The "height" of the triangle is r and the "base" is \( r \delta \theta \). The horizontal distance of the centroid of the elemental sector from the origin (more correctly, from the "pole" of the polar coordinate system) is \( \frac{2}{3} r \cos \theta \) . The first moment of area of the sector with respect to the \(y \) axis is
