The midpoint rule for the triple integral ∭ B f ( x , y , z ) d V over the rectangular solid box B is a generalization of the midpoint rule for double integrals. The region B is divided into subboxes of equal sizes and the integral is approximated by the triple Riemann sum ∑ i = 1 l ∑ j = 1 m ∑ k = 1 n f ( x i ¯ , x j ¯ , z k ¯ ) Δ V is ( x i ¯ , y j ¯ , z k ¯ ) the center of the box and V is the volume of each subbox. Apply the midpoint rule to approximate ∭ B x 2 d V over the solid B = { ( x , y , z ) | 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1 } by using a partition of eight cubes of equal size. Round your answer to three decimal places.
The midpoint rule for the triple integral ∭ B f ( x , y , z ) d V over the rectangular solid box B is a generalization of the midpoint rule for double integrals. The region B is divided into subboxes of equal sizes and the integral is approximated by the triple Riemann sum ∑ i = 1 l ∑ j = 1 m ∑ k = 1 n f ( x i ¯ , x j ¯ , z k ¯ ) Δ V is ( x i ¯ , y j ¯ , z k ¯ ) the center of the box and V is the volume of each subbox. Apply the midpoint rule to approximate ∭ B x 2 d V over the solid B = { ( x , y , z ) | 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1 } by using a partition of eight cubes of equal size. Round your answer to three decimal places.
The midpoint rule for the triple integral
∭
B
f
(
x
,
y
,
z
)
d
V
over the rectangular solid box B is a generalization of the midpoint rule for double integrals. The region B is divided into subboxes of equal sizes and the integral is approximated by the triple Riemann sum
∑
i
=
1
l
∑
j
=
1
m
∑
k
=
1
n
f
(
x
i
¯
,
x
j
¯
,
z
k
¯
)
Δ
V
is
(
x
i
¯
,
y
j
¯
,
z
k
¯
)
the center of the box and V is the volume of each subbox. Apply the midpoint rule to approximate
∭
B
x
2
d
V
over the solid
B
=
{
(
x
,
y
,
z
)
|
0
≤
x
≤
1
,
0
≤
y
≤
1
,
0
≤
z
≤
1
}
by using a partition of eight cubes of equal size. Round your answer to three decimal places.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY