Integrand

Definition

The integrand is the function being integrated in an integral. It appears inside the integral symbol and is the main focus of the integration process.

5 Must Know Facts For Your Next Test

1. In a definite integral, the integrand is evaluated over a specific interval $[a,b]$.
2. The integrand can be any continuous function, which ensures that the integral exists.
3. Changing the integrand affects the value of both definite and indefinite integrals.
4. In applications, the choice of integrand often represents a physical quantity like velocity or area density.
5. Techniques such as substitution or integration by parts are used to simplify complex integrands.

Review Questions

• What role does the integrand play in an integral?
• How does changing the integrand affect a definite integral?
• Describe one technique used to simplify complex integrands.

Related terms

Definite Integral: An integral with specified upper and lower limits, representing the area under the curve of the integrand within those limits.

Indefinite Integral: An integral without specified limits, representing a family of functions whose derivative is the given integrand.

Integration by Parts: A technique for integrating products of functions by splitting them into parts and applying a specific formula.