Steps to Find the Limits of Integration
To find the limits of integration, we can use the following steps for any integral.
- First, we solve the integration problem by figuring out the antiderivative of a function, represented as ∫abf(x).dx = [F(x)]ab.
- The second step is applying the limits [a, b] to the antiderivative.
- This means substituting the values of a and b into the antiderivative. The final result is obtained by subtracting F(a) from F(b), expressed as [F(x)] evaluated from a to b i.e., F(a) − F(b).
In simple terms, the limits of integration help us find the specific numerical value of the given integral expression.
How to Find Upper and Lower Limit of Integration
If you are given a definite integral like ∫ab f(x) dx, where f(x) is the function and a and b are the limits of integration, then:
- a is the lower limit of the integration, and
- b is the upper limit of the integration.
Limit of Integration
Limits of integration are the numbers that set the boundaries for calculating the definite integral of a function. The definite integral, ∫f(x)dx, involves finding the antiderivative F(x) and then evaluating it at the upper and lower limits, [a, b].
In this article, we will cover the basic concept of integration, formulas for limits of integration, the meaning of integration, how to change limits, how to find limits, and the application of limits of integration. At the end of this article, you will learn about the limits of integration by the solved examples provided and practice questions to test the learning for yourself.
Table of Content
- What is Integration?
- What are the Limits of Integration?
- How to Change the Limits of Integration?
- Formulas of Limits of Integration
- Application of Limits of Integration