Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the primary use of integration in calculus?

1. Finding limits

2. Finding areas under curves

3. Simplifying functions

4. Differentiating polynomials

The correct answer is: Finding areas under curves

The primary use of integration in calculus is indeed finding areas under curves. This concept is central to the fundamental theorem of calculus, which links differentiation and integration. When we integrate a function, we are essentially summing up infinitesimal pieces of area under that curve over a specified interval. This application is vital in various fields, such as physics, engineering, and economics, where determining the total quantity represented by a curve is necessary. For example, if you have a function that describes the velocity of a moving object over time, integrating that function provides the total distance traveled by that object within a given time frame. This is because the area under the velocity-time curve represents the distance. Thus, the integration process is essential for calculating such quantities accurately, which is why it is primarily associated with finding areas under curves.