Question

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 Bijk. Use the Midpoint Rule to estimate the value of the integral. Divide B into eight sub-boxes of equal size. (Round your answer to three decimal places.) cos(xyz) dV, where B = {(x, y, z) | 0 ≤ x ≤ 5, 0 ≤ y ≤ 5, 0 ≤ z ≤ 5} B

Answer #1

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
Bijk.
Use the Midpoint Rule to estimate the value of the integral.
Divide B into eight sub-boxes of equal size. (Round your
answer to three decimal places.)
cos(xyz) dV, where B = {(x, y, z) | 0 ≤ x ≤ 2, 0 ≤...

Evaluate the triple integral.
2 sin (2xy2z3) dV, where
B
B =
(x, y, z) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 2, 0 ≤ z ≤ 1

57.
a. Use polar coordinates to compute the (double integral (sub
R)?? x dA, R x2 + y2) where R is the region in the first quadrant
between the circles x2 + y2 = 1 and x2 + y2 = 2.
b. Set up but do not evaluate a double integral for the mass of
the lamina D={(x,y):1≤x≤3, 1≤y≤x3} with density function ρ(x, y) =
1 + x2 + y2.
c. Compute??? the (triple integral of ez/ydV), where E=
{(x,y,z):...

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