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fxdung
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In physics we often change a sum to an integral.But I am not clear when can we change a sum to an integral?When a term of sum is comparable to the sum,can we change the sum to integral?
A sum is a mathematical operation that adds together a finite number of terms. An integral, on the other hand, is a mathematical operation that finds the area under a curve or the volume of a solid. In other words, a sum is a discrete operation while an integral is a continuous operation.
A sum can be changed to an integral when the number of terms in the sum becomes infinitely large. This is because an integral is a continuous operation that can handle an infinite number of terms, while a sum can only handle a finite number of terms.
Changing a sum to an integral allows us to solve more complex problems that involve continuous functions. It also allows us to find more accurate solutions by considering an infinite number of terms instead of just a finite number.
We can change a sum to an integral by taking the limit of the sum as the number of terms approaches infinity. This is known as the Riemann sum, and it is the basis for finding the area under a curve or the volume of a solid using integrals.
Changing a sum to an integral has many real-life applications, including calculating the distance traveled by an object with varying velocity, finding the amount of medication in a person's bloodstream over time, and determining the total cost of a continuous function, such as a water bill or electricity bill.