Integrals Teacher Resources
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The Fundamental Theorems of Calculus
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.
Twelfth graders explore integral calculus. In this Calculus lesson, 12th graders use the tools of integral calculus to investigate the motion of a free falling objet which is governed by both gravity and air resistance.
The Io Plasma Torus
In this plasma torus worksheet, students solve 5 problems including finding the dimensions of the Io torus, determining the formula for the volume of a torus, finding the actual volume of the Ion torus and finding the amount of sodium atoms in the torus. Students are given an integral calculus problem where they use the 'washer method' to find the formula for the volume of a torus.
Riemann Sums and the Fundemental Theorem of Calculus
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.
Definite Integrals and Area Under a Curve
Young scholars explore the concept of definite integrals. In this definite integrals instructional activity, students find the area between two curves. Young scholars use the Ti-Nspire to find the definite integrals of curves such as sine and cosine.
Why we Use Theorem In Calculus
Students read an article to explain the reasoning behind theorems. In this calculus lesson, 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.
Calculus for electric circuits
In this circuits activity students complete a series of questions on equations, robotics and integration. There is an answer sheet.
Twelfth graders investigate the limitations of the Fundamental Theorem of Calculus. In this calculus lesson plan, 12th graders explore when one can and cannot use the Fundamental Theorem of Calculus and explore the definition of an improper integral.
Exploring Functions with Calculus and Dynamic Software
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.
Sum of Rectangle Areas to Approximate Integrals
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.
What is the Number "e"?
Students explore natural logarithms. In this calculus lesson, students investigate exponential growth and integral calculus which leads to the natural logarithm function. Students solve problems involving exponential growth.
Area Under the Curve with TI InterActive! Document
Students explore the area under the curve using the TI InterActive! document. In this calculus lesson, students input various functions and create tables. They answer questions based on their results.
Calculating Arc Lengths of Simple Functions-I
In this calculating arc lengths worksheet, students are given 4 simple functions and they use the Pythagorean Theorem and the basic techniques of calculus to find the arc-length formula in order to find the arc-length.
Wind, Pressure, Force, Calculus and Engineering Connections
Twelfth graders solve first order differential equations using the separation of variables technique. In this calculus lesson, 12th graders explain the connection between math and engineering. They brainstorm what engineers do in real life.
Approximating Integrals with Riemann Sums
Learners 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.
Applications of Integrals
Twelfth graders investigate applications of integration. In this Calculus lesson, 12th graders use the TI-89 to explore various problem solving techniques including symbolic, graphical, and numeric methods of solving applications of integrals.
Calculus Practice Test: Velocity, Functions
In this calculus learning exercise, 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 learning exercise contains 14 problems.