Integration tables

Definition

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

5 Must Know Facts For Your Next Test

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

Review Questions

• What types of functions are commonly found in integration tables?
• How can integration tables speed up the process of solving integrals?
• Why might you use an integration table instead of performing an integral manually?

Related terms

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

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

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