The law of definite integral product is an important concept in calculus, which describes that the definite integral products of two functions are equal to the definite integral products of these two functions respectively. This rule is very useful in solving some mathematical problems, especially when dealing with area and volume.

First of all, the product rule of definite integral can be used to calculate the definite integral of the product of two functions. For example, we have two functions f(x) and g(x), and we can use the product law of definite integrals to calculate the definite integral of their product F(x)=f(x)g(x). This is very useful in calculating the definite integral of complex variable function, because it can simplify complex problems into simpler ones.

Secondly, the product rule of definite integral can be used to calculate the definite integral of the product of multivariate functions. For example, we have three functions f(x), g(x) and h(x), and we can calculate the definite integral of their product F(x)=f(x)g(x)h(x) by using the product rule of definite integral. This is very useful when dealing with the product of multiple functions, because it can simplify complex problems into simpler ones.

In addition, the product rule of definite integral can also be used to calculate the definite integral of compound function of function. For example, if we have a function f(x) and a function g(x), we can calculate the definite integral of the compound function F(x)=g[f(x)] by the product rule of definite integral. This is very useful when dealing with definite integrals of composite functions, because it can simplify complex problems into simpler ones.

Generally speaking, the product law of definite integral is a very powerful tool, which can help us solve many complicated mathematical problems. Knowing and mastering this law can better understand and solve various mathematical problems.