- #1
rado5 said:Please tell me if I am wrong. I suspect about the ranges. Are my range corrrect?
Quinzio said:The quantity you integrate (that is '1') is always positive.
An integral is basically a sum, so a sum of positive terms cannot turn into something negative.
The result of the book [tex](1-\sqrt2 \cong -0.41) [/tex] is negative, so it is wrong.
A double integral in polar coordination is a type of integral that is used to find the volume or area of a region in the polar coordinate system. It involves integrating over a two-dimensional shape that is expressed in terms of polar coordinates (r, θ).
A regular double integral involves integrating over a two-dimensional shape in the Cartesian coordinate system (x, y). In contrast, a double integral in polar coordination involves integrating over a two-dimensional shape in the polar coordinate system (r, θ).
The limits of integration for a double integral in polar coordination depend on the shape of the region being integrated. The inner integral typically has limits of 0 to 2π, representing a full revolution around the origin. The outer integral has limits that correspond to the outer boundary of the region.
The formula for calculating a double integral in polar coordination is ∫∫f(r, θ)rdrdθ, where f(r, θ) is the function being integrated and r and θ are the polar coordinates.
Double integrals in polar coordination are commonly used in physics and engineering to calculate the mass, moment of inertia, and center of mass of objects with circular or cylindrical symmetry. They are also used in calculus to solve problems related to areas, volumes, and surface areas in polar coordinates.