How to read integrals out loud

  1. How do you read $\int f(x)\, dx = g(x)?$

    Answer:

    The integral of $f(x)$ with respect to $x$ equals $g(x)$. (Reminder, $f(x)$ is read "F - of - X.")
  2. How do you read $$\int_a^b f(x)\, dx = S?$$

    Answer:

    The definite integral of $f(x)$ from $a$ to $b$ equals $S$.
  3. What is the $f(x)$ in $$\int f(x)\, dx$$ called?

    Answer:

    An "integrand."
  4. What is the $f(x)$ in $$\int_a^b f(x)\, dx$$ called?

    Answer:

    Still called an "integrand."
  5. What is the $b$ in $$\int_a^b f(x)\, dx$$ called?

    Answer:

    The "upper limit of the integral." Or just simply, "upper limit."
  6. What is the $a$ in $$\int_a^b f(x)\, dx$$ called?

    Answer:

    The "lower limit of the integral." Or just simply, "lower limit."
  7. What is the $C$ in $$\int 3x^2\,dx = x^3 + C$$ called?

    Answer:

    An "integration constant."