Evaluating a Triple Iterated Integral In Exercises 3-10, evaluate the triple iterated integral.
∫
0
2
∫
0
1
∫
−
1
2
x
y
z
3
d
x
d
y
d
z
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.
Electric charge is distributed over the triangular region D shown below so that the charge density at (x, y)
is σ(x, y) = 4xy, measured in coulumbs per square meter (C/m²). Find the total charge on D. Round
your answer to four decimal places.
1
U
5
4
3
2
1
1
2
5
7
coulumbs
Let E be the region bounded cone z = √√/6 - (x² + y²) and the sphere z = x² + y² + z² . Provide an
answer accurate to at least 4 significant digits. Find the volume of E.
Triple Integral
Spherical Coordinates
Cutout of sphere is for visual purposes
0.8-
0.6
z
04
0.2-
0-
-0.4
-0.2
04
0
0.2
0.2
x
-0.2
04 -0.4
Note: The graph is an example. The scale and equation parameters may not be the same for your
particular problem. Round your answer to 4 decimal places.
Hint: Solve the cone equation for phi.
* Oops - try again.
The temperature at a point (x,y,z) of a solid E bounded by the coordinate planes and the plane
9.x+y+z = 1 is T(x, y, z) = (xy + 8z +20) degrees Celcius. Find the average temperature over
the solid. (Answer to 4 decimal places).
Average Value of a function
using 3 variables
z
1-
y
Hint: y = -a·x+1
* Oops - try again.
x
Chapter 14 Solutions
Student Solutions Manual For Larson/edwards? Multivariable Calculus, 11th
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