Integration tables Definition - Calculus II Key Term

Definition

Integration tables are pre-compiled lists of integrals of various functions. They serve as a reference to help solve complex integrals quickly.

Integration tables often include common integral forms such as polynomial, trigonometric, exponential, and logarithmic functions.
Using integration tables can save time compared to solving integrals from scratch using techniques like substitution or integration by parts.
They usually provide solutions for both indefinite and definite integrals.
Some tables include special functions like hyperbolic functions and their integrals.
Integration tables are particularly useful when dealing with non-elementary integrals that do not have simple antiderivatives.

Indefinite Integral: $\int f(x) \, dx$ represents the family of all antiderivatives of $f(x)$.

$\int_{a}^{b} f(x) \, dx$ calculates the net area under $f(x)$ from $x=a$ to $x=b$.

$F(x)$ is an antiderivative of $f(x)$ if $F'(x) = f(x)$.