Definite Integral of Constant/Corollary

Corollary to Definite Integral of Constant

$\ds \int_a^b \rd x = b - a$


Proof

From Definite Integral of Constant:

$\ds \int_a^b c \rd x = c \paren {b - a}$

where $c$ is a constant.


Setting $c = 1$:

$\ds \int_a^b \rd x = b - a$

$\blacksquare$


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): definite integral
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): definite integral
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