Double integral is the integral of binary function in space, which is similar to definite integral and is the limit of some form of sum. The essence is to find the volume of a curved top cylinder. Multiple integrals have a wide range of applications, which can be used to calculate the area of curved surface, the center of gravity of plane thin plate and so on. The double integral of plane region can be extended to the integral on the (directed) surface in high-dimensional space, which is called surface integral.
Extended data
To calculate the double integral in polar coordinates, it is necessary to express the integrand function f(x, y), integral area d and area element dσ in polar coordinates. The polar coordinate form of the function f(x, y) is f(rcosθ, rsinθ).
In order to get the transformation of the area element dσ in polar coordinates, the coordinate curve network is used to divide D, that is, the circle with r=a, that is, O as the center and the ray with θ=b, O as the starting point are infinitely divided D, and let δ σ be the small areas from R to r+dr and θ to θ+dθ, and its area is
Double integral, like definite integral, is not a function, but a numerical value. Therefore, if a continuous function f(x, y) contains a double integral, the specific value of this double integral can be solved by two integrals.