The most basic calculation method of the first kind of surface integral is to convert it into double integral, just like the second kind of surface integral.

The most basic method of the second kind of surface is to turn it into a double integral by finding the projection. I want to remind you that if the surface is a part of x=c, then x'=0, that is, dx=0, so the surface integral includes dxdy and dzdx, which are directly zero.

Moreover, the integral about P(x, y, z)dzdx also becomes the integral of P(c, y, z)dydz, and then the combination direction can become a double integral. The same is true for the case where y or z is constant.

Second, the integration targets are different.

The first curve integral is arc length integral, and the integral element of arc length curve integral is arc length element; The second curve integration is the integration of coordinates (the projection of the directed arc length on the coordinate axis), and the integral element of the curve integration of the coordinate axis is the coordinate element.

Three. Different applications

The first curve integral can solve the problems such as the quality of linear objects with uneven density, and the second can solve the problems such as doing work.

Baidu Encyclopedia-First Curve Integral

Baidu Encyclopedia-Ⅱ Curve Integral