Integrand

Definition

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

5 Must Know Facts For Your Next Test

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

Review Questions

• What is the role of the integrand in a definite integral?
• How does the nature of an integrand affect your choice of integration technique?
• What might you need to consider if an integrand has discontinuities within your interval of integration?

Related terms

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

Antiderivative: 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.