Introduction to Polar Coordinate
Double Integrals over Polar Coordinate (r, θ)
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 polar coordinate (r, θ) using the following conversion formula
Conversion Formula from 2-dimensional Cartesian Coordinate to Polar Coordinate| x = rcosθ, y = rsinθ, where 0≤θ≤2π x2+ y2 = r2, ∫R∫ f(x, y) dA = ∫R∫ f(r, θ) rdrdθ |
Type "Polar G1" fo in phone app.
https://www.geogebra.org/calculator/ebc5gsny
Question 1
By using polar integral, find the area of region enclosed by four-petaled r=sin2.