Light

Term-by-term Integration

Definition

Term-by-term integration refers to integrating each term in a series individually. It allows us to integrate each term separately without affecting the other terms.

Analogy

Imagine you have different ingredients for making cookies, such as flour, sugar, and chocolate chips. When you mix them together, you can't separate them anymore. However, with term-by-term integration, it's like being able to take out and integrate each ingredient individually.

Related terms

Constant of Integration: When we integrate a function, there is always an arbitrary constant added at the end because derivatives lose information about constants. This constant is known as the constant of integration.

Definite Integral: A definite integral represents finding the exact area under a curve between two specific points. It gives us a numerical value as the result.

U-Substitution: U-substitution is a technique used to simplify integrals by making a substitution with a new variable. It helps transform complex integrals into simpler ones that are easier to solve.