- #1
Vadim
- 15
- 0
just want to know if [tex]\int f(x)g(x)=\int f(x) * \int g(x)[/tex]
Integral equality refers to the mathematical concept that states the integral of a product of two functions is equal to the product of their integrals. In other words, if we have two functions f(x) and g(x), the integral of their product, ∫f(x)g(x), is equal to the product of their individual integrals, ∫f(x) * ∫g(x).
Integral equality is significant because it allows us to simplify and solve complex integration problems. By breaking down a product of functions into the product of their individual integrals, we can use known integration techniques to solve the problem more easily.
Yes, integral equality can be applied to all functions as long as they are continuous and integrable. This means that the function must be defined and have a finite integral over the interval of integration.
Yes, there are some special cases where integral equality does not hold. For example, if the functions f(x) and g(x) are not continuous or if their product is not integrable over the interval of integration, then integral equality cannot be applied.
Integral equality is closely related to the fundamental theorem of calculus, which states that the integral of a function f(x) can be evaluated by finding its antiderivative F(x) and evaluating it at the upper and lower limits of integration. In the case of integral equality, we can think of the product of two functions as the composition of their antiderivatives, which is then evaluated at the limits of integration.