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double integral help please?
Area Density: f(x, y) = x + y
Quarter Circle: x^2 + y^2 =< 4, x > 0, y > 0
what is the mass
can't figure out what the bounds would be
1 Answer
- kbLv 79 years agoFavorite Answer
Use polar coordinates (so that θ is in [0, π/2], the first quadrant).
So, the mass equals
∫∫ (x+y) dA
= ∫(θ = 0 to π/2) ∫(r = 0 to 2) (r cos θ + r sin θ) * (r dr dθ), via polar coordinates
= ∫(θ = 0 to π/2) (cos θ + sin θ) dθ * ∫(r = 0 to 2) r^2 dr
= [(sin θ - cos θ) {for θ = 0 to π/2}] * [(1/3)r^3 {for r = 0 to 2}]
= 2 * 8/3
= 16/3.
I hope this helps!
