Integrals Teacher Resources

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Are your calculus pupils aware that they are standing on the shoulders of giants? This lesson provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The calculus controversy paper is not included but one can find a number of good resources on the Internet regarding the development of calculus and the role of Newton and Leibnez. 
Students explore integral calculus.  In this calculus lesson, students explore the relationship between the area under the graph of a functions and the integral of the function.  Students also discover the rule for the integral of f(x)=ax^n.
Learners investigate integral calculus.  In this calculus lesson plan, students investigate the relationship between the area above and below the curve using integral calculus.  Learners look for a general rule for area above: area below. 
Students explore the Fundamental Theorem of Calculus. In the Calculus lesson, students investigate indefinite and definite integrals and the relationship between the two, which leads to the discovery of the Fundamental Theorem of Calculus. 
Twelfth graders investigate integration.  In this Calculus lesson, 12th graders explore indefinite and definite integrals.  Students use technology (TI-89) to verify the solutions to problems requiring integration by parts.
Students integrate integrals.  In this integrating integrals lesson, students integrate definite and indefinite integrals.  Students use their Ti-89 to find the integrals of cubic, inverse, and trigonometric function graphs on a given interval.
Students investigate the volume of a solid.  In this calculus activity, students use integration to find the volume of a solid generated by a region, the Orion crew module. 
Learners read an article to explain the reasoning behind theorems. In this calculus lesson plan, students understand the underlying principles of theorems and how it helps them make sense of the problems. They know why they do what they do in AP Calculus.
Twelfth graders solve first order differential equations using the separation of variables technique. In this calculus lesson plan, 12th graders explain the connection between math and engineering. They brainstorm what engineers do in real life.
Twelfth graders explore integral calculus.  In this calculus lesson, 12th graders explore the volume and surface area of an ellipse in the context of an Easter egg problem. 
Students explore the concept of definite integrals.  In this definite integrals activity, students find the area between two curves.  Students use the Ti-Nspire to find the definite integrals of curves such as sine and cosine.
Students explore the area under the curve using the TI InterActive! document.  In this calculus activity, students input various functions and create tables. They answer questions based on their results.
Twelfth graders investigate the limitations of the Fundamental Theorem of Calculus.  In this calculus instructional activity, 12th graders explore when one can and cannot use the Fundamental Theorem of Calculus and explore the definition of an improper integral.    
Calculus can be project-based and inquiry-centered by using dynamic software.
Students use a graphing calculator to do calculations and edit their calculations using script. In this graphing calculator lesson, students compute the length of intervals given in parametric form. Students verify the results for specific given functions and define the critical points where the first derivative is found.
Students explore the concept of approximating integrals.  In this approximating integrals lesson, students approximate integrals by finding the area of rectangles.  Students use a graphing calculator to find the left, right, and midpoint riemann sums. 
Students investigate integral calculus.  In this calculus instructional activity, students explore an application of integrations through a leaking hot tub problem.  The activity emphasizes using the integral of a rate of change to give the accumulated change.
Students practice calculating and analyzing Riemann sums and illustrate when Riemann sums will over/under-approximate a definite integral. They view how the convergence of Riemann sums as the number of subintervals get larger.
Twelfth graders investigate applications of integration.  In this Calculus lesson plan, 12th graders use the TI-89 to explore various problem solving techniques including symbolic,  graphical,  and numeric methods of solving applications of integrals. 
In this calculus worksheet, students observe graphs and identify the limits of the functions listed in the graph. They determine the definite integrals and derivatives. Students use the trapezoid rule to estimate distance. This five-page worksheet contains 14 problems.

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