Final answer:
In calculus, using spherical coordinates to evaluate a triple integral is useful for symmetrical functions like e^-(x²+y²+z²). Spherical coordinates involve r, θ, and φ, which simplify the function and volume element for integration.
Step-by-step explanation:
The subject of this question is related to evaluating a triple integral using spherical coordinates. In the context of mathematics and particularly calculus, when encountering an integral of a function like e-(x²+y²+z²), it is often advantageous to use spherical coordinates due to the symmetrical nature of the function with respect to the origin.
The conversion to spherical coordinates involves rewriting the variables x, y, and z in terms of r (the radial distance from the origin), θ (the polar angle from the z-axis), and φ (the azimuthal angle from the x-axis), with the relationships x = r sin(θ)cos(φ), y = r sin(θ)sin(φ), and z = r cos(θ), where r≥ 0, 0 ≤ θ ≤ π, and 0 ≤ φ < 2π
This simplifies the function and associated volume element for integration purposes. The triple integral is then evaluated over the appropriate limits for r, θ, and φ which are determined by the extent of the region of integration.