Related Topics:

More Lessons for Calculus

Math Worksheets

In this lesson, we introduce the Fundamental Theorem of Calculus.

**What is the Fundamental Theorem of Calculus?**

**The Fundamental Theorem of Calculus, Part 1**

If*f* is continuous on [*a*, *b*], then the function *g* is defined by

**The Fundamental Theorem of Calculus**

The fundamental theorem of Calculus is an important theorem relating antiderivatives and definite integrals in Calculus. The fundamental theorem of Calculus states that if a function f has an antiderivative F, then the definite integral of f from a to b is equal to F(b)-F(a). This theorem is useful for finding the net change, area, or average value of a function over a region.

The Fundamental Theorem of Calculus Part 1
The Fundamental Theorem of Calculus Part 2

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Calculus

Math Worksheets

In this lesson, we introduce the Fundamental Theorem of Calculus.

If

is continuous on [*a*, *b*] and differentiable on (*a*, *b*), and *g*'(*x*) = *f*(*x*)

** The Fundamental Theorem of Calculus, Part 2 **

If *f * is continuous on [*a, b*], then

where *F* is any antiderivative of *f*, that is, a function such that *F *’ = *f*

** Example: **

Find the area under the parabola *y* = *x*^{2} from 0 to 1.

** Solution: **

An antiderivative of *f *(*x*) = *x*^{2} is

Use Part 2 of the Fundamental Theorem to find the required area *A*.

The fundamental theorem of Calculus is an important theorem relating antiderivatives and definite integrals in Calculus. The fundamental theorem of Calculus states that if a function f has an antiderivative F, then the definite integral of f from a to b is equal to F(b)-F(a). This theorem is useful for finding the net change, area, or average value of a function over a region.

The Fundamental Theorem of Calculus Part 1

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

[?] Subscribe To This Site