The Fundamental Theorem of Calculus

Connecting Derivatives and Integrals

Part 1: The Accumulation Function

An integral accumulates area under a curve. Let .

Drag the slider to find the area when .

x = 0 x = 6
Area =
check_circle Target Area Reached!

Part 1: The Magic Trick

The derivative of an integral gives you back the original function! The cancels the .

Drag onto the integral to cancel it.

Now drag the variable to replace the dummy variable .

FTC Part 1 Complete!

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Part 2: Evaluating Integrals

Definite integrals can be solved using the antiderivative:

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Part 2: Build the Solution

Evaluate the definite integral by dragging the correct pieces into the formula.

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Drag pieces to build

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Master of Calculus!

You've successfully connected derivatives and integrals using both parts of the Fundamental Theorem of Calculus.