Odd please 21-30. Cartesian to polar coordinates. Evaluate the following integrals using polar coordinates. Assume (r, θ) are polar coordinates. A sketch is helpful.
21. ∫∫(x² + y²) dA; R = {(r, θ): 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π}
22. ∫∫2xy dA; R = {(r, θ): 1 ≤ r ≤ 3, 0 ≤ θ ≤ π/2}
23. ∫∫2xy dA; R = {(x, y): x² + y² ≤ 9, y ≥ 0}
24. ∫∫dA; R = {(x, y): x² + y² ≤ 9}
25. ∫∫(1 + x² + y²) dA; R = {(r, θ): 1 ≤ r ≤ 2, 0 ≤ θ ≤ π}
26. ∫∫(x² + y²)^(3/2) dy dx; R = {(x, y): x² + y² ≤ 4, x ≥ 0, y ≥ 0}
27. ∫∫(x² + y²)^(3/2) dy dx; R = {(x, y): x² + y² ≤ 9}
28. ∫∫√(9 - 7√(x² + y²)) dy dx
