You can use polar coordinates instead of rectangular coordinates. Geometrically, the integration result is a volume surrounded by an integration function and an integration region. The integral region can be infinitely divided into smaller regions.

In polar coordinates, the geometric meaning of binary function is the same, that is, the volume surrounded by binary function and domain. The integration area is uncertain. In most cases, first of all, given the angle, the integral R. Due to the introduction of trigonometric function, the integral object becomes complicated.

When converting to quadratic integration, it is usually to integrate R first, and then to integrate θ. Sometimes things change.

Extended data

1, when the region d is a circle, a sector, a ring or a part thereof, the integrand function is f(x? +y？ ), f(x/y), f(y/x), double integral can be calculated in polar coordinates.

2. In the calculation of double integral, how to choose the order of the second integral is a key point. Usually, the order that can make the quadratic integration simpler can be selected according to the structural characteristics of the graph.

3. When calculating the second integral, when integrating the first integral variable, the second variable should be regarded as a constant that has nothing to do with it.

Baidu Encyclopedia-Double Integral