Understanding Integrals: A Basic Question on Integral Calculus

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In summary, an integral is a mathematical concept that represents the area under a curve on a graph and is used to find the total amount or accumulated value of a changing quantity. There are two types of integrals: definite, which has specific limits and gives a specific answer, and indefinite, which has no limits and gives a family of answers. Integrals can be solved using various methods, such as substitution, integration by parts, and trigonometric substitution. Derivatives and integrals are inverse operations, with derivatives representing the rate of change of a function and integrals representing the total change or accumulation of a function. Integrals have various real-life applications in fields such as physics, engineering, economics, and statistics, and can be used
  • #1
mnb96
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Hello,
this is a very basic question on integral calculus, but I have a doubt.
If f is a one-variable function from reals to reals, what is the meaning (if any) of computing:

[tex]\int^{b}_{a}f(x)(dx)^2[/tex]

Thanks.
 
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  • #2
No meaning at all.
 
  • #3
No answer ? LOL
 
  • #4
Above post is an answer. Furthermore, it's correct :smile: What else would anyone want? There is simply no definition of such combination of symbols.
 

FAQ: Understanding Integrals: A Basic Question on Integral Calculus

What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total amount or accumulated value of a changing quantity over a given interval.

What is the difference between a definite and indefinite integral?

A definite integral has specific limits and represents a specific numerical value, while an indefinite integral has no limits and represents a function. In other words, a definite integral gives a specific answer, while an indefinite integral gives a family of answers.

How do you solve an integral?

Integrals can be solved using various methods, such as substitution, integration by parts, and trigonometric substitution. It is important to first identify the type of integral and then use the appropriate method to solve it.

What is the relationship between derivatives and integrals?

Derivatives and integrals are inverse operations. A derivative represents the rate of change of a function, while an integral represents the total change or accumulation of a function. In other words, the derivative is the slope of a function, and the integral is the area under the curve of that function.

How are integrals used in real-life applications?

Integrals are used in a wide range of fields, including physics, engineering, economics, and statistics. They are used to calculate areas, volumes, and other quantities in real-life scenarios. For example, integrals can be used to calculate the amount of work done by a force, the total distance traveled by an object, or the total revenue generated by a business.

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