Definite Integrals (Leaving Cert Mathematics): Flashcards

Specific numerical value

Net area under curve from $x=a$ to $x=b$

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

Antiderivative of $f(x)$

Integrate absolute value of function

$\int_a^b [f(x)+g(x)] \, dx = \int_a^b f(x) \, dx + \int_a^b g(x) \, dx$

$\int_a^b c \cdot f(x) \, dx = c \cdot \int_a^b f(x) \, dx$

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

$0$

$\int_a^b f(x) \, dx + \int_b^c f(x) \, dx = \int_a^c f(x) \, dx$

Limits

Always cancels

$-\cos(x) + C$

Displacement, work, energy