Evaluate the double integral ∬Dcossqrt(x2+y2)dA, where D is the disc with center the origin and radius 2, by changing to polar coordinates.

Answer 1

Region D in polar coordinates: {r ≤ 2, 0 ≤ θ≤ 2π}. dA = rdrdθ.

∬Dcossqrt(x2+y2)dA = ∫₀^2πdθ∫₀²rcosrdr = θ₀^2π(rsinr + cosr)₀² = 2π(2sin2 + cos2 - 1)