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.

Answer 1

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

Answer 2

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