∫[f(u)±g(u)]du
The expression you provided, ∫[f(u)±g(u)]du, represents the integral of a function that is either the sum or the difference of two other functions f(u) and g(u), with respect to the variable u
The expression you provided, ∫[f(u)±g(u)]du, represents the integral of a function that is either the sum or the difference of two other functions f(u) and g(u), with respect to the variable u.
To evaluate this integral, you can use the linearity property of integration. The linearity property states that the integral of a sum or difference of functions is equal to the sum or difference of their individual integrals.
If the expression is a sum, then the integral can be written as:
∫[f(u) + g(u)]du = ∫f(u)du + ∫g(u)du
In this case, you can simply evaluate the integral of f(u) and g(u) separately, and their individual answers add up.
If the expression is a difference, then the integral can be written as:
∫[f(u) – g(u)]du = ∫f(u)du – ∫g(u)du
Again, you can evaluate the integrals of f(u) and g(u) separately, and their individual answers subtract.
To clarify, the integral of a function with respect to a variable represents the area under the graph of the function between two specified limits. The notation ∫ (used for the integral) is an elongated “S,” and the du at the end indicates the variable of integration.
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