The integral notation ##\int_{a}^{x} f(t)dt## is essential for clarity in mathematical expressions, as it distinguishes the variable of integration from the limits of integration. Using the same variable, such as ##x##, for both the upper limit and the integrand leads to confusion. The correct formulation emphasizes that ##t## is the variable of integration, while ##a## and ##x## are constants defining the limits. This distinction is crucial for accurate mathematical communication.
PREREQUISITESStudents of calculus, mathematics educators, and anyone involved in mathematical writing or notation who seeks to improve clarity and precision in their work.
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