The discussion revolves around the notation used in integral calculus, specifically questioning why the integral should be expressed as ##\int_{a}^{x} f(t)dt## instead of ##\int_{a}^{x} f(x)dx##. Participants explore the implications of variable naming in integrals and the potential for confusion that arises from using the same variable for different meanings.
Participants express disagreement regarding the correct notation for integrals, with some supporting the use of ##t## and others questioning the implications of variable naming. The discussion remains unresolved as no consensus is reached on the preferred notation.
Participants highlight the importance of variable distinction in integrals, but the discussion does not resolve the underlying assumptions about notation conventions or the implications of variable choice.
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.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 $$\sum_{k = 1}^k a_k$$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