well derivatives cannt be used without limits so it is application for calculus
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No, but you can use physics to show students practical applications to the math that they are learning
It tells you the area of the function (curve) between the two limits.
The integral of a given function between given integration limits will always be a constant. The integral of a given function between variable limits - for example, from 0 to x - can only be a constant if the function is equal to zero everywhere.
Limits (or limiting values) are values that a function may approach (but not actually reach) as the argument of the function approaches some given value. The function is usually not defined for that particular value of the argument.