Evaluate the integral by changing to cylindrical coordinates. 5) ??? ??^?(25 - y²) ?^?_?(x² + y²) xz dz dy dx
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Recall that in cylindrical coordinates, we have: x = r cos(θ) y = r sin(θ) z = z dx dy dz = r dr dθ dz Now, we can rewrite the given integral in cylindrical coordinates: ∫∫∫ (25y^2 + 5xz) dz dy dx = ∫∫∫ (25(r sin(θ))^2 + 5(r cos(θ))(r sin(θ))z) r dr dθ dz Now, Show more…
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