1. [15 points] Rewrite the following iterated triple integral using cylindrical coordinates and evaluate.\\ $\int_{-2}^{2} \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \int_{\sqrt{x^2+y^2}}^{2} (x^2 + y^2)dzdydx$
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In cylindrical coordinates, we have: x = r*cos(theta) y = r*sin(theta) z = z The Jacobian determinant for the conversion is r. So, the integral becomes: ∫∫∫ (r^2) dz dy dx = ∫∫∫ (r^2) r dz dy dx Show more…
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