Asking about integral notation

In summary, using the same variable for both the upper limit and the variable of integration in an integral can cause confusion and is not considered a correct notation. Instead, a different variable should be used for the upper limit, such as using ##t## in ##\int_{a}^{x} f(t)dt##. Similarly, in a sum, the variable used for the summation index should be different from the one used for the terms being summed.
  • #1
songoku
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TL;DR Summary
Why writing $$\int_{a}^{x} f(x) dx$$ is not correct?
Why should it be ##\int_{a}^{x} f(t)dt## ?

Couldn't it be like this:
Let F(x) = ##\int f(x)dx## so ##\int_{a}^{x} f(x)dx## = F(x) - F(a)

Thanks
 
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  • #2
songoku said:
Summary: Why writing $$\int_{a}^{x} f(x) dx$$ is not correct?

Why should it be ##\int_{a}^{x} f(t)dt## ?

Couldn't it be like this:
Let F(x) = ##\int f(x)dx## so ##\int_{a}^{x} f(x)dx## = F(x) - F(a)

Thanks
The integral ##\displaystyle{\int_a^b f(t)\,dt}## is short for ##\displaystyle{\int_{t=a}^{t=b} f(t)\,dt}.## If you use the same letter (##b=t##) for two different meanings then you cause confusion.
 
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  • #3
songoku said:
Summary: Why writing $$\int_{a}^{x} f(x) dx$$ is not correct?

Why should it be ##\int_{a}^{x} f(t)dt## ?

Couldn't it be like this:
Let F(x) = ##\int f(x)dx## so ##\int_{a}^{x} f(x)dx## = F(x) - F(a)

Thanks
Why is it not correct to write $$\sum_{k = 1}^k a_k$$
 
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  • #4
Thank you very much for the explanation fresh_42 and PeroK
 

Related to Asking about integral notation

1. What is integral notation?

Integral notation is a mathematical notation used to represent the concept of integration, which is a mathematical operation that calculates the area under a curve or the volume of a solid. It is often denoted by the symbol ∫ and is used to represent the integral of a function.

2. How is integral notation used?

Integral notation is used in calculus to solve problems involving finding the area under a curve or the volume of a solid. It is also used in physics and engineering to solve problems related to motion, work, and energy. In general, it is a powerful tool for solving problems involving continuous quantities.

3. What is the difference between indefinite and definite integral notation?

An indefinite integral is represented by the symbol ∫ followed by the function to be integrated, while a definite integral is represented by the same symbol but with the upper and lower limits of integration included. Indefinite integrals result in a family of solutions, while definite integrals result in a single numerical value.

4. How do you evaluate an integral using integral notation?

To evaluate an integral, you must first identify the function to be integrated and then use the appropriate integration rules and techniques to solve it. This may involve substitution, integration by parts, or other methods. Once the integral is solved, the result can be expressed using integral notation.

5. Can integral notation be used for multivariable functions?

Yes, integral notation can be used for multivariable functions. In this case, the integral is evaluated over a region in space rather than a single variable. This is known as a multiple integral and is represented by multiple integral symbols, with each representing a different variable of integration.

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