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More Lessons for Calculus

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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

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

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