Let us evaluate the triple integral ∭B f(x,y,z)dV where f(x,y,z) = xz with ranges of integration as 3≤x≤24, 0≤y≤2, and 0≤z≤2.
To solve this, we perform the integration successively over z, y, and x.
Starting with z, we integrate the function xz over the range 0 to 2 for z:
∫(from 0 to 2) xz dz. The result is xz^2 / 2 when evaluated from 0 to 2 which simplifies to 2x.
Next, we integrate the obtained result ∫(from 0 to 2) 2x dy over y. But since the function does not depend on y, the integral simplifies to 4x evaluated from 0 to 2.
Finally, we evaluate ∫(from 3 to 24) 4x dx over the range of x. This yields 2x^2 when evaluated from 3 to 24.
On subtracting the lower limit from the upper limit, we get:
= 2*(24)^2 - 2*(3)^2
= 2*576 - 2*9
= 1134
Therefore, the value of the triple integral ∭B f(x,y,z)dV over the specified function and boundaries is 1134.