Show that ∫ − ∞ ∞ ∫ − ∞ ∞ ∫ − ∞ ∞ x 2 + y 2 + z 2 e - ( x 2 + y 2 + z 2 ) dx dy dz = 2π (The improper triple integral is defined as the limit of a triple integral over a solid sphere as the radius of the sphere increases indefinitely.)
Solution Summary: The author explains that the value of the integral is equal to 2pi .
∫
−
∞
∞
∫
−
∞
∞
∫
−
∞
∞
x
2
+
y
2
+
z
2
e-(x2+y2+z2) dx dy dz = 2π (The improper triple integral is defined as the limit of a triple integral over a solid sphere as the radius of the sphere increases indefinitely.)
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.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY