Area Under a Curve Teacher Resources

There’s no limit to what your calculus class can accomplish when you’re working with Lesson Planet!

Our teacher team has curated a variety of ways to teach calculus students how to calculate the area under a curve. A video connects the concepts of area and slope in a straightforward way, and an AP Calculus video uses four rectangles to demonstrate the concept. Learners can also take their knowledge online with an interactive resource that uses left-hand sums.

Apply integration and area in practical ways with a lesson that follows a curvy road to calculate the area under a curve, or a velocity activity that connects physics, calculus, and robots. Finish up your unit with an assessment that prompts class members to calculate a data set with normal distribution in two different ways.

Want an in-depth unit on integral calculus? Check out a series that incorporates technology into a study of derivatives and antiderivatives. Or look below for our full collection of related materials, perfect for any calculus class!

Showing 1 - 24 of 187 resources
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Finding The Area Under a Curve Using Rectangles

For Students 11th - Higher Ed
Here's an AP Calculus video that provides a discussion on determining an approximate for the area under a curve by calculating the sum of areas of rectangles that is smaller than the area and by finding the sum of areas of rectangles...
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Lesson #94 Exact Area Under a Curve

For Teachers 10th - 12th
Students research Riemann Sums. In this area lesson students listen to a lecture on finding the area under a curve. Links to a song about Riemann Sums, and a song titled "Failing My Calculus" are included.
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Exploring the Area Under a Curve

For Teachers 9th - 12th Standards
Using TI-89, mathematicians explore and investigate Riemann sums to estimate the area under the graphs of intervals by drawing and illustrating rectangles. They review and practice the concepts of summation notation and area formulas to...
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Definite Integrals and Area Under a Curve

For Teachers 11th - Higher Ed
Students explore the concept of definite integrals.  In this definite integrals lesson, students find the area between two curves.  Students use the Ti-Nspire to find the definite integrals of curves such as sine and cosine.
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Filling The Urn

For Teachers 9th - 12th Standards
Students calculate the area under a curve. In this calculus instructional activity,students calculate the area by integrating the equation. They calculate the volume of cylindrical shapes created between graphs.
1 In 1 Collection
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Investigating Area Under a Curve

For Teachers 9th - 11th Standards
Taking a activity straight from the calculus classroom and making it algebra appropriate is the task of the day. Learners go step by step through calculating different area approximations underlines and curves, reviewing many key...
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Three Derivative Application Problems

For Students 12th - Higher Ed
In this calculus derivative worksheet, students solve one area under a curve problem, one tangent line problem, and one area problem.  This worksheet involves derivatives of trig functions.
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Area Under A Curve

For Teachers 9th - 11th
Calculus students 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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InteGreat

For Teachers 9th - Higher Ed Standards
Hands-on investigation of Riemann sums becomes possible without intensive arithmetic gymnastics with this interactive lesson plan. Learners manipulate online graphing tools to develop and test theories about right, left, and midpoint...
14:56
Lesson Planet

Area under a Graph

For Students 8th - 12th Standards
What? The calculation of area is a linear distance? A short video shows how to use the areas of simple polygons to estimate the area under a graph. Pupils divide the area under a curve into figures to easier calculate the area. Given...
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Interactive Calculus Tool

For Students 9th - 12th
It's almost like a graphing calculator, but it's completely free. An interactive allows users to graph a polynomial function on a coordinate plane. Additionally, the program can draw tangent lines, draw derivative curves, and calculate...
12:38
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What Does Area Have to Do with Slope? | Essence of Calculus, Chapter 9

For Students 11th - Higher Ed
It seems like area and slope wouldn't have any connection. Here is a video that explains how to find the average value of a function over an interval. It connects the area under a curve to the slope of the antiderivative curve.
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Area Sums: Estimation with Rectangles

For Students 11th - Higher Ed
The more rectangles, the better the estimate. Using the interactive, pupils explore estimating the area under a curve using left-hand sums. Learners respond to challenge questions on how to get better estimates using the same technique.
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The Area Function

For Teachers 11th - 12th
Students explore the concept of area under a curve.  In this area under a curve lesson, students find integrals of various functions.  Students use their Ti-Nspire to graph functions and find the area under the curve using the...
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Quartic Regions

For Teachers 11th - 12th
Students explore the concept of quartic regions.  In this quartic regions instructional activity, students find the area under a curve using their Ti-89 calculator.  Students find definite integrals of two curves.  Students determine the...
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Area Under the Curve with TI InterActive! Document

For Teachers 11th - 12th
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.
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Are Kitchen Cabinets at the Correct Height? Lessons 1-5

For Teachers 9th - 12th Standards
Here's a not-so-normal unit on normal heights. Future statisticians anonymously collect class data on female heights, weights, and shoe sizes. They then analyze the data using normal distributions, z-scores, percentiles, and the...
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Trapezoidal and Midpoint Approximations: Area of a Skirt

For Students 11th - Higher Ed
When are trapezoids better than rectangles? Using trapezoids pupils approximate the area of fabric defined by a function. Just like with rectangles, learners realize the more trapezoids the more accurate the approximation. Scholars use...
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Area Under the Normal Curve

For Students 9th - 12th Standards
Use more than one method to find the area under the normal curve. Given a data set with normal distribution, pupils calculate the proportion of scores between values two different ways—once by using a standard normal distribution table...
5:38
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Approximating Area Using Rectangles

For Students 11th - Higher Ed
Finding area using rectangles—isn't that a little too simplistic for a calculus course? Viewers learn how to approximate area under a curve using rectangles in the first installment of a seven-part video series on the definite integral....
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Finding the Area Under A Curve with Random Probability

For Teachers 11th - Higher Ed
Young scholars explore the concept of area under a curve. In this area under a curve lesson, students find the area under a curve using the Monte Carlo method using random points and probability. Young scholars calculate the area under...
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The Definite integral and Area Under a Curve

For Teachers 11th - 12th
Students define integrals and explore how they relate to the areas under a curve. In this calculus lesson plan, students solve word problems relating curves and integrals. They sing a song to help them remember the formula for the area...
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The Fundamental Theorem of Calculus and Area Under the Curve

For Teachers 12th
Twelfth graders review the fundamental theorem of calculus and solve for the area under the curve. In this calculus lesson, 12th graders differentiate between the area under the curve and the definite integral as it related to the...
Lesson Planet

Roller Coaster Robot

For Teachers 10th - 12th
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.

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Area Under a Curve