Integrand Definition - Calculus II Key Term

Definition

An integrand is the function being integrated in an integral. It is the expression inside the integral sign.

The integrand is denoted as $f(x)$ in a definite integral $\int_{a}^{b} f(x)\, dx$.
The properties of the integrand determine the techniques used for integrating, such as substitution or integration by parts.
If the integrand has discontinuities within the interval of integration, special methods like improper integrals may be required.
Polynomial, trigonometric, exponential, and logarithmic functions are common types of integrands found in calculus problems.
Understanding the behavior of the integrand (e.g., symmetry, periodicity) can simplify solving definite integrals.

A type of integral with upper and lower limits that represents the signed area under a curve from $a$ to $b$.

A function whose derivative is equal to the given function; finding it is a key step in indefinite integration.

$u$-Substitution: $u$-substitution is a technique for evaluating integrals by simplifying them into a more easily manageable form.