Evaluate the triple integral using only geometric interpretation and symmetry. 38 . ∭ B ( z 3 + sin y + 3 ) d V , where B is the unit ball x 2 + y 2 + z 2 ≤ 1
Evaluate the triple integral using only geometric interpretation and symmetry. 38 . ∭ B ( z 3 + sin y + 3 ) d V , where B is the unit ball x 2 + y 2 + z 2 ≤ 1
Solution Summary: The author evaluates the integral using geometric interpretation and symmetry. The volume of the sphere is 4pi .
Evaluate the triple integral using only geometric interpretation and symmetry.
38.
∭
B
(
z
3
+
sin
y
+
3
)
d
V
,
where B is the unit ball x2 + y2 + z2 ≤ 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 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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