Use cylindrical coordinates. Evaluate ∫∫∫ (x^2 + y^2) dV, E where E is the region that lies inside the cylinder x^2 + y^2 = 9 and between the planes z = -2 and z = 3.
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Step 1: Set up the triple integral using cylindrical coordinates: \[ \iiint_E (x^2 + y^2) dV = \int_{0}^{\pi} \int_{0}^{3} \int_{-2}^{3} r^2 \cdot r \, dz \, dr \, d\theta \] Show more…
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