Triple Integral

Calculus Level 4

Compute the triple integral of f ( r , θ , z ) = r 2 f(r,\theta, z) = r^2 over the region R R bounded by the paraboloid r 2 = 9 − z r^2= 9-z and the plane z = 0 z=0 .


The answer is 381.703.

Jose Sacramento by Jose Sacramento , 66, Portugal

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1 solution

Otto Bretscher
Mar 3, 2016

∫ 0 2 π ∫ 0 3 ∫ 0 9 − r 2 r 2 × r d z d r d θ = 243 2 π ≈ 381.7 \int_{0}^{2\pi}\int_{0}^{3}\int_{0}^{9-r^2}r^2\times r dzdrd\theta= \frac{243}{2}\pi\approx 381.7

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Highly correct! Performing the integral in cylindric coordinates I got the same result whereat the determination of the integration area was happily ;-) not so difficult in this case.

Andreas Wendler - 5 years, 3 months ago

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