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Calculus

Fundamental Theorem

The Fundamental Theorem of Calculus brings the two big ideas of calculus together by establishing a definite integral functions as providing an antiderivatives of any continuous function (First Fundamental Theorem). This in turn provides a means of using antiderivatives to evaluate definite integrals (Second Fundamental Theorem). The natural logarithm function is an important example of the Fundamental Theorem in action.

Calculus: Fundamental Theorem Activities

Title Type

Area Function Demo

Connect the area under a derivative curve to the graph of the antiderivative.

Alignments  Standards  |  Textbook  
  • 4702

Area Function Problems

Understand the relationship between the area under a derivative curve and the antiderivative function.

Alignments  Standards  |  Textbook  
  • 4667

The First Fundamental Theorem of Calculus

Make visual connections between a function and its definite integral.

Alignments  Standards  |  Textbook  
  • 5427

The Second Fundamental Theorem of Calculus

Students make visual connections between a function and its definite integral.

Alignments  Standards  |  Textbook  
  • 4938

Natural Logarithm

Construct the graph of the natural logarithm function from its definition.

Alignments  Standards  |  Textbook  
  • 4691

Applied Fundamental Theorem of Calculus

For a given function, students recognize the accumulation function as an antiderivative of the original function, and identify the graphical connections between a function and its accumulation function.

Alignments  Standards  |  Textbook  
  • 3021
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