Definition:Definite Integral/Limits of Integration/Lower Limit
Definition
Let $a, b \in \R$ be real numbers such that $a \le b$.
Let $f: \R \to \R$ be a real function.
Let the definite integral of $f$ with respect to $x$ from $a$ to $b$ be:
- $\ds \int_a^b \map f x \rd x$
The limit $a$ is referred to as the lower limit of the integral.
Also see
Technical Note
The $\LaTeX$ code for \(\intlimits {\dfrac {\map f s} s} {s \mathop = 1} {s \mathop = a}\) is \intlimits {\dfrac {\map f s} s} {s \mathop = 1} {s \mathop = a} .
When the expression being evaluated fits into the line and does not expand upwards or downwards much, the square brackets become similarly small, so making the expression difficult to read, thus:
The $\LaTeX$ code for \(\intlimits {\map f s} {s \mathop = 1} {s \mathop = a}\) is \intlimits {\map f s} {s \mathop = 1} {s \mathop = a} .
Hence we have another command that uses bigger square brackets:
The $\LaTeX$ code for \(\bigintlimits {\map f s} {s \mathop = 1} {s \mathop = a}\) is \bigintlimits {\map f s} {s \mathop = 1} {s \mathop = a} .
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{VI}$: On the Seashore
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): definite integral
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integration
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): lower limit (of integration)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): limit of integration
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): lower limit