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Calculus

Definite Integrals and Applications

The definite integral is the other “big idea” of calculus and this unit provides lessons to build a foundation of understanding of the definition of the definite integral as a limit of Riemann Sums, ways of approximating definite integrals, and an understanding of the errors in those approximations. Applications of the definite integral include those of finding volumes and average values of functions.

Calculus: Definite Integrals and Applications Activities

Title Type

Riemann Sums

Visualize values for different Riemann sums and use these values to estimate the area of a region.

Alignments  Standards  |  Textbook  
  • 7065

Riemann Rectangle Errors

Use three Riemann sums used to estimate the area of a plane region.

Alignments  Standards  |  Textbook  
  • 4804

Definite Integral

Make visual connections between the definite integral of a function and the signed area between the function and the x-axis.

Alignments  Standards  |  Textbook  
  • 6173

Piecewise Linear Integral

Use graphical interpretations of the meanings of definite integrals and definite integral functions.

Alignments  Standards  |  Textbook  
  • 4500

Average Value

Examine areas as integrals and as rectangles for given functions.

Alignments  Standards  |  Textbook  
  • 4865

MVT for Integrals

Demonstrate how the average value of a function over an interval is related to the definite integral.

Alignments  Standards  |  Textbook  
  • 4843

Trapezoid and Midpoint Rules

Use visual representation of area estimation methods in order to determine which is most accurate.

Alignments  Standards  |  Textbook  
  • 5117

Solids of Revolution - Disks

Use visual representation of solids of revolution to find the exact volume of the solid.

Alignments  Standards  |  Textbook  
  • 5537

Visualizing Solids of Revolution - Washers

Use visual representation of solids of revolution to find the exact volume of the solid.

Alignments  Standards  |  Textbook  
  • 5453
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