Evaluate the surface integral ∬ σ f x , y , z d S f x , y , z = x + y + z ; σ is the surface of the cube defined by the inequalities 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1.
Evaluate the surface integral ∬ σ f x , y , z d S f x , y , z = x + y + z ; σ is the surface of the cube defined by the inequalities 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1.
f
x
,
y
,
z
=
x
+
y
+
z
;
σ
is the surface of the cube defined by the inequalities
0
≤
x
≤
1
,
0
≤
y
≤
1
,
0
≤
z
≤
1.
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.
Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the other two on the positive y-axis and the negative x-axis where the diagonal has length L = 3, occurs when the angles at both (other) vertices are π/4. Include a sketch.
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evaluate
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