At this point we have three “different” integrals.

At this point we have three different “integrals.” Let’s see if we can sort out the differences.

Indefinite integrals

An indefinite integral, also called an antiderivative computes classes of functions: Here there are no limits of integration, and your answer will have a “” at the end. Pay attention to the notation:

PIC
Where .
Two students, say Devyn and Riley, are working with the following indefinite integral: Devyn computes the integral as and Riley computes the integral as Which student is correct?
Devyn is correct Riley is correct Both students are correct Neither student is correct

Accumulation functions

An accumulation function, also called an area function computes accumulated area: This is a function of whose derivative is , with the additional property that . Pay attention to the notation:

PIC
Where .
True or false: There exists a function such that
true false

Definite integrals

A definite integral computes signed area: Here we always have limits of integration, both of which are numbers. Moreover, definite integrals have definite values, the signed area between and the -axis. Pay attention to the notation:

PIC
Where .