Practice: Triple Integrals in Cylindrical Coordinates (1)

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Triple Integration (cylindrical)

5 Activities

Evaluate ∫05∫−5−x20∫x2+y2−119−3x2−3y2(2x−3y)dzdydx\displaystyle\int_{0}^{\sqrt{5}}\int_{-\sqrt{5-x^2}}^{0}\int_{x^2+y^2-11}^{9-3x^2-3y^2}(2x-3y)dzdydx∫05​​∫−5−x2​0​∫x2+y2−119−3x2−3y2​(2x−3y)dzdydxusing cylindrical coordinates.

Answer

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More Triple Integration (cylindrical) Questions:

Practice: Triple integration (cylindrical)

Write down an integral using cylindrical coordinates representing ∭Eln⁡(x2+y2+z2)   ⁣dV\displaystyle\iiint_E\ln(x^2 + y^2 + z^2) \ \de{V}∭E​ln(x2+y2+z2)  dV  where EEE is the region inside the cylinder x2+y2=4x^2 + y^2 = 4x2+y2=4, outside the cylinder x2+y2=1x^2 + y^2 = 1x2+y2=1, and inside the sphere x2+y2+z2=9x^2 + y^2 + z^2 = 9x2+y2+z2=9.