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