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Integrals involving Trig Substitution
Twelfth graders solve derivatives using trig substitution. In this trigonometry lesson, 12th graders integrate integrals by substituting trig values into the equations. They review detailed examples before solving problems on their own.
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MVT for Integrals
Students identify the meaning of the Mean Value Theorem. In this calculus instructional activity, students solve problems using the definite integral. They calculate the average value of a function.
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Introduction to Integration
Students discuss the importance of Integrals as it relates to calculus. In this calculus lesson, students define Integrals and practice taking the integrals of polynomials. They work problems to enhance their understanding of how...
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Integration Formulas
Twelfth graders review differential formulas and find their corresponding integration formula. In this calculus lesson, 12th graders review differential and integral formulas as it pertaining to solving calculus problems. They develop...
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Review of Techniques of Integration
Twelfth graders review techniques of integration. In this calculus activity, 12th graders review integration by parts, integrals with powers, trig substitution, and simpson's rule for a chapter 8 test. They review with a right angle...
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Summary of Techniques of Integration
Learners define and review techniques for integration by parts. In this calculus lesson, students solve rational expression using integration and apply the partial fraction rule. They practice solving problems online.
Project Maths
Integral Calculus
From derivatives to antiderivatives and back again. Building on the second lesson of the three-part series covering functions, learners explore the concept of an antiderivative. They connect the concept to the graph of the function and...
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Shortest Path
High schoolers explore an application of definite integrals. They graph three functions that go through the same three points. Learners use the symbolic capacity of their calculators to find the shortest path through the three points and...
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Filling The Urn
Students calculate the area under a curve. In this calculus lesson,students calculate the area by integrating the equation. They calculate the volume of cylindrical shapes created between graphs.
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Disc/Washer Method
Students calculate the volume of solids. In this calculus instructional activity, students apply the Disk and Washer Method to solve for the volume of three dimensional objects. They calculate the volume caused by rotation that create...
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Highs and Lows
Solve problems using integration and derivatives. By using calculus, learners will analyze graphs to find the extrema and change in behavior. They then will identify the end behavior using the derivatives. Activities and handouts are...
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What is an Antiderivative? Slope Fields
Students take the derivative of a function. For this calculus lesson, students define slope fields and what they are used for. They relate slope fields to the real world.
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Roller Coaster Robot
Students calculate the area under a curve. In this calculus lesson, students use Riemann sums to find and approximate the area under a curve. They use the derivative and differential equations to solve.
Texas Instruments
Listen and Line Up
High schoolers practice the derivative using an interactive activity. In this calculus lesson they explore the derivative by playing a game. Each student gets a turn at being the caller.
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Gateway Arc Length
Learners differentiate and calculate the length of an arc. They define an arc and relate it to the area of a circle and integrate the function to solve the equations. Young scholars use their TI calculators to graph the equation.
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The Region Between Two Curves
Learners find the area of a region between two curves. They integrate functions such as sin(x) and cos(x) on a given interval and find the area bounded by the two functions. Pupils use their TI-89 to aid them in finding the bounded...
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Riemann Rectangle Errors
Learners calculate the area under a curve. In this calculus lesson, students integrate the function to find the area under the curve. They use the Ti to create a visual of the graph.
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Inverse Trigonometric Functions (Review)
Students discuss the importance of inverse functions and derivatives. In this calculus lesson, students analyze inverse trig functions by solving for missing angles. They graph the functions and discuss integration by parts.
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Riemann Sums
Students calculate the area under a curve. For this calculus lesson, students use Riemann Sums to find the area under a curve. They apply the boundaries of intervals as they solve for each area.
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Differential Equations
Students solve derivatives of differential equations. In this calculus lesson, students solve equations using the derivative to obtain no differentials in the equation. They complete an assignment in the text book also.
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Average Value of a Function
Students investigate the average value of a function given different interval values. In this calculus lesson, students explore word problems and apply their knowledge of average value to find the answer. They apply previous knowledge to...
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Solids of Revolution - Disks
Young mathematicians solve the volume using the disk method in this calculus lesson. They revolve a graph around the x-axis and calculate the volume. They use the TI to see the revolving around the x-axis and create a virtual cross...
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Area Under A Curve
Calculus learners use the derivative and integral to solve problems involving areas. They calculate the area under a curve as they follow a robot off road making different curves along the drive, using Riemann Sums and Trapezoidal rules...
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Review for Test on sections 6.2-6.3
Twelfth graders review integration techniques to get ready for their test. For this calculus lesson, 12th graders review integrals, trig substitution, integration by parts, trapezoidal rules and simpson's rule in preparation for a test....