[justify]When dealing with non-rectangular regions, especially those predominantly in circular shapes, performing double integrals in the traditional rectangular coordinates (x, y) can become rather tedious. To simplify the integration process, we convert the 2-dimensional Cartesian coordinate (x, y) to [b]polar coordinate[/b] (r, θ) using the following conversion formula[br][/justify][b][u]Conversion Formula from 2-dimensional Cartesian Coordinate to Polar [b]Coordinate[/b][/u][br][/b][table][tr][td]x = rcosθ,[br]y = rsinθ, where 0≤θ≤2π[br]x[sup]2[/sup]+ y[sup]2[/sup] = r[sup]2[/sup],[br][br][b]∫[sub]R[/sub]∫ f(x, y) dA = ∫[sub]R[/sub]∫ f(r, θ) rdrdθ[/b][br] [/td][/tr][/table][br]
Type "Polar G1" fo in phone app.[u][br][color=#0000ff]https://www.geogebra.org/calculator/ebc5gsny[/color][/u]
By using polar integral, find the area of region enclosed by four-petaled r=sin2[math]\theta[/math].
[math]\frac{\pi}{2}[/math]unit[sup]2[/sup]