Evaluate the triple integral
(3 integrals and with lower range E)xyz dV
where E is the solid: 0 ≤ z ≤ 3, 0 ≤ y ≤ z, 0 ≤ x ≤ y.

Question

Evaluate the triple integral 
(3 integrals and with lower range E)xyz  dV
where E is the solid: 0 ≤ z ≤ 3, 0 ≤ y ≤ z, 0 ≤ x ≤ y.

turingtest · Answer

$$\int\limits \int\limits \int\limits xyzdV=\int\limits_{0}^{3}\int\limits_{0}^{z}\int\limits_{0}^{y}xyzdxdydz$$$$=\int\limits\limits_{0}^{3}\int\limits\limits_{0}^{z}{y^3\over2}zdydz=\int\limits\limits_{0}^{3}{z^5\over8}dz={3^6\over48}={243\over16}$$

anonymous · Answer

thanks for explaining too ! some people just give me the answer which is useless