Average Value In Exercises 63-66, find the average value of the function over the given solid region. The average value of a continuous function f(x, y, z) over a solid region is Average value = 1 V ∭ Q f ( x , y , z ) d V where V is the volume of the solid region Q. f ( x , y , z ) = x + y over die solid bounded by the sphere x 2 + y 2 + z 2 = 3
Average Value In Exercises 63-66, find the average value of the function over the given solid region. The average value of a continuous function f(x, y, z) over a solid region is Average value = 1 V ∭ Q f ( x , y , z ) d V where V is the volume of the solid region Q. f ( x , y , z ) = x + y over die solid bounded by the sphere x 2 + y 2 + z 2 = 3
Solution Summary: The author calculates the average value of the function f(x,y,z)=x+y over the solid region Q.
Average Value In Exercises 63-66, find the average value of the function over the given solid region. The average value of a continuous function f(x, y, z) over a solid region is
Average
value
=
1
V
∭
Q
f
(
x
,
y
,
z
)
d
V
where V is the volume of the solid region Q.
f
(
x
,
y
,
z
)
=
x
+
y
over die solid bounded by the sphere
x
2
+
y
2
+
z
2
=
3
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
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