"University calculus"-chaper13-multiple integral-Sanchong integral introduction

To undertake before the introduction of a heavy integral and double integral, here we naturally lead to triple integral.

In the introduction of the double integral, we have buried a small foreshadowing, the geometric meaning of the double integral is to solve a volume, but we only limited to the geometry of the curved top cylinder, then for the completely surface D wrapped in the space d ', how can we find its volume?

Naturally, we can think of the x, Y, z three dimensions as parallel lines, and then the d ' is divided into n small cuboid, such as.

With n tending to infinity, we can perfectly get the volume of the d ' region.

Personally, this example is only to naturally lead to the concept and form of triple integrals, in practical applications, it is difficult to calculate the volume of a variety of irregular geometry (because you can not accurately characterize the boundary d in the form of domain definition), these things the author will be in detail in the post-order article.

In order to keep the form of triple integrals consistent with the form of two integrals and the Riemann sum of one integral, we can describe the triplet integral as the following Riemann and form:

"University calculus"-chaper13-multiple integral-Sanchong integral introduction