Polar coordinates

• How to Integrate This Double Integral in Polar Coordinates
  Convert the circular region to polar bounds, include the Jacobian, and evaluate the double integral to obtain π/16.
• How to Set Up a Double Integral Over x² + y² ≤ 4 in Polar Coordinates
  The region x² + y² ≤ 4 is a disk of radius 2; set its polar bounds and multiply the transformed integrand by r.
• What Is the Area Bounded by $r=|\sin\theta|$?
  For the polar curve r = |sin θ|, integrating over 0 ≤ θ ≤ 2π gives total area π/2; each lobe encloses π/4.
• Find z Given Arg(z + 1) = π/6 and Arg(z − 1) = 2π/3
  The two argument conditions define rays from −1 and 1. Their intersection is z = 1/2 + (√3/2)i, as direct substitution verifies.