Integral, why antiderivative is area under curve

In summary, an integral is a mathematical concept used to find the total value of a function over a specific range by representing the accumulation of a quantity over an interval. An antiderivative is the inverse function of a derivative and is used in integration to find the original function. The antiderivative and integral are closely related, with the fundamental theorem of calculus stating that the integral can be found by evaluating the antiderivative at the upper and lower bounds of the interval. The antiderivative is referred to as the area under the curve because it represents the accumulation over an interval, which can be interpreted as the area under the curve of the function. Integrals and antiderivatives have various real-world applications in fields such as physics, engineering
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kidsasd987
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well, no it makes sense. sorry. I will delete this thread
 

1. What is an integral?

An integral is a mathematical concept that represents the accumulation of a quantity over a given interval. It is used to find the total value of a function over a specific range, and is often interpreted as the area under the curve of the function.

2. What is an antiderivative?

An antiderivative is the inverse function of a derivative. In other words, it is a function that can be differentiated to give the original function. It is used in integration to find the original function when given its derivative.

3. How is the antiderivative related to the integral?

The antiderivative and integral are closely related concepts. The fundamental theorem of calculus states that the integral of a function can be found by evaluating its antiderivative at the upper and lower bounds of the interval. In other words, the integral is the antiderivative of a function evaluated at two points.

4. Why is the antiderivative referred to as the area under the curve?

The antiderivative is often referred to as the area under the curve because the integral represents the accumulation of a quantity over an interval, which can be interpreted as the area under the curve of the function. This is a visual way of understanding the concept of integration.

5. What are some real-world applications of integrals and antiderivatives?

Integrals and antiderivatives have various applications in fields such as physics, engineering, economics, and statistics. They can be used to calculate areas, volumes, and physical quantities such as work and distance. In economics, they are used to model and analyze supply and demand curves. In statistics, they are used to find probabilities and to analyze data sets.

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