Answer to Question #121488 in Calculus for trishnarjun kunamalla

Question

Let D={(x,y,z)∈ℝ3:x2+y2≤a2 and 0≤z≤b}
where a
and b
are positive constants. The answer to ∭D2zdV
is

Answer 1

$\iiint_D2zdV=\int^{2\pi}_0d\theta\intop^a_0rdr\int^b_02zdz=$

$=b^2\int^{2\pi}_0d\theta\intop^a_0rdr=\frac {a^2b^2}{2}\int^{2\pi}_0d\theta=$

$=\frac {a^2b^2}{2}\cdot2\pi=\pi a^2b^2$