(a) Use the Midpoint Rule for double integrals (see Section 15.... | Filo

Estimate a definite integral using midpoint and trapezoid rules.

SOLVED:(a) In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a triple integral over a box B, where f(x, y, z) is evaluated at the center (xi, yj, zk) of the box Bi j k . Use the Midpoint Rule to estimate ∬B √(x^2 y^2 z^2) d V, where B is the cube defined by 0 ⩽x ⩽4,0 ≤y ≤4,0 ⩽z ⩽4 . Divide B into eight cubes of equal size. (b) Use a computer algebra system to approximate the integral in part (a) correct to the nearest integer. Com- pare with the answer to par