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12th Grade Math

(10 Units, 104 Lessons)

Unit 6 - The Integral(9 Lessons)

Introducing the Integral

12th Grade Math

» Unit:

The Integral

Big Idea:What is an integral? How are integrals related to derivatives? Today we begin connecting these seemingly unrelated ideas in Calculus.

19 Resources

2 Favorites

19 Resources

2 Favorites

u-Substitution (Part 1 of 2)

12th Grade Math

» Unit:

The Integral

Big Idea:Integrate sin(x)cos(x). Double angle sine? Or treat cos(x) like the chain rule? Today we introduce u-substitution to “undo” the chain rule.

17 Resources

3 Favorites

17 Resources

3 Favorites

u-Substitution (Part 2 of 2)

12th Grade Math

» Unit:

The Integral

Big Idea:Can there ever be several choices for u that work? Today we explore various options and considerations for productive choices for u.

23 Resources

1 Favorites

23 Resources

1 Favorites

Rectangular Approximation Methods

12th Grade Math

» Unit:

The Integral

Big Idea:Computing area under linear functions is easy. But what about curvy functions? Summing an infinite number of rectangles offers a solution.

22 Resources

2 Favorites

22 Resources

2 Favorites

RAM and the Definite Integral

12th Grade Math

» Unit:

The Integral

Big Idea:An infinite number of rectangles? Of zero width? Today students make connections between RAM and evaluating definite integrals.

20 Resources

1 Favorites

20 Resources

1 Favorites

In-Depth with Definite Integrals

12th Grade Math

» Unit:

The Integral

Big Idea:What if limits of integration are switched? What if one limit is a variable? Today students reason about properties of definite integrals.

16 Resources

0 Favorites

16 Resources

0 Favorites

Connections and Applications of Definite Integrals

12th Grade Math

» Unit:

The Integral

Big Idea:Why does the Evaluation Theorem work? What is a function’s average y-value? Today we investigate applications of definite integrals.

21 Resources

0 Favorites

21 Resources

0 Favorites

Approximating Definite Integrals from Tables

12th Grade Math

» Unit:

The Integral

Big Idea:Do Riemann Sums still work with unequal rectangle widths? What if we do not know the function’s equation? You betcha…

18 Resources

0 Favorites

18 Resources

0 Favorites

Integration Review for Semester Exam

12th Grade Math

» Unit:

The Integral

Big Idea:Heading into the semester exam, we take a day to recap the various integration techniques and applications we have learned so far.

18 Resources

0 Favorites

18 Resources

0 Favorites