The integral of the sum of the terms is equal to the sum of the integral of each term.*TRUEFALSE

The statement "The integral of the sum of the terms is equal to the sum of the integral of each term" is TRUE.

Explanation

This is a direct application of the linearity of integration, which states that:

$\int (f(x) + g(x)) \, dx = \int f(x) \, dx + \int g(x) \, dx$

This property holds for integrals over the same interval. In general, if you have a finite sum of functions, you can integrate term by term:

If $f_1(x), f_2(x), \ldots, f_n(x)$ are functions, then:

$\int (f_1(x) + f_2(x) + \cdots + f_n(x)) \, dx = \int f_1(x) \, dx + \int f_2(x) \, dx + \cdots + \int f_n(x) \, dx$

This classification as true applies regardless of the specific functions involved, so the integral operator distributes over addition, confirming that the initial statement is indeed true.