Highlight the process of mathematical discovery for your classes. This lesson examines the development of the Fundamental Theorem of Calculus over time. Understanding the history of the theorem helps create a better understanding of the...

In this integral test worksheet, students use the integral test to determine the upper and lower bounds for a given function. They identify the convergence of a series. This one-page worksheet contains four multi-step problems.

In this interval worksheet, students find integrals of functions, use the first derivative test to classify points, and find the local and global extrema. This one-page worksheet contains eight multi-step problems.

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...

An informative module highlights eight polynomial concepts. Learners work with polynomial functions, expressions, and equations through graphing, simplifying, and solving. 

In this integral activity, students categorize the given twelve integrals to determine which of the four basic integral functions provided each follows.

Accumulate the content so far. Learners review the content from the first five lessons dealing with accumulation functions. The eight problems go over finding maximums, minimums, concavity, points of inflection, and intervals of increase...

In this function worksheet, students identify functions, express decimals as fractions and write decimals as a geometric series. This one-page worksheet contains six multi-step problems.

Learners calculate the area under a curve. In 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.

For this graphing functions worksheet, students solve four problems where they graph given functions, find the sum related to the area under the curve and determine an integral.

In this definite integrals instructional activity, learners find the definite integrals of 16 functions.  Students find definite integrals for a given interval in order to find the name of Maxwell Smart's partner.

In the Riemann sums worksheet, students use Riemann sums to estimate the area under a curve. They calculate intervals and subintervals. Students create a graph picturing the intervals. This seven-page worksheet contains explanations...

In this integral test, students determine the limits, give partial sums of infinite series, explore geometric series, and use the Integral Test to determine if a function converges. This two-page worksheet contains six multi-step problems.

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...

In this math worksheet, students use Euler's Method to solve differential equations. They are given an equation to graph (y'). Students sketch that equation as well as the related equation (y). They find the area of given rectangles and...

In this calculating arc lengths worksheet, learners 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.

In this integral worksheet, students use Riemann sums to estimate their answers. They answer story (or word) problems about distance/speed. Students are given a defined interval and use the Riemann sum to find the endpoints of the graph....

For this integration worksheet, students graph a function that is a quarter circle curve. They calculate lengths of curves by approximation using the distance formula. Students use a computer program to calculate the approximation of the...

In this Simpson's Rule activity, students use the Fundamental Theorem of Calculus to determine the antiderivatives and evaluate integrals. They find the midpoint of given polygons and sketch the graph of the function. This nine-page...

In this Euler's Method and Riemann's Sum worksheet, students identify the best situation in which to use Euler's Method and Riemann's Sum. They identify the initial value of a problem and use the accumulation formula to determine the...

Keep moving along a curve. Two items in the set of released free-response questions from the 2010 AP® Calculus BC exam involve movement along a graph. One involves particle motion along a polar curve while the other uses a squirrel...

In this integral worksheet, students use the Riemann Sum to estimate the value of a function. This two-page worksheet contains two problems.

In this function learning exercise, students evaluate sums, estimate the area of the region between graphs, estimate the volume of a hemisphere, and use subintervals and the limit definition integrals to evaluate functions. This two page...

In this indefinite integral worksheet, students compute the volume of a solid located between planes. They evaluate the average value of functions over a given interval and sketch functions. Students find the sum of numbers in a...