The Fundamental Theorem of Calculus and the Definite Integral (VCE SSCE Mathematical Methods): Flashcards

Includes arbitrary constant $c$

Signed area under curve

Above: positive; Below: negative

$\int_a^b f(x)dx = G(b) - G(a)$

Evaluate at $b$ minus evaluate at $a$

Cancels out when subtracting

Changes sign to negative

$0$

$\int_a^b = \int_a^c + \int_c^b$

$\int_a^b kf(x)dx = k\int_a^b f(x)dx$