Lesson #94 Exact Area Under a Curve

Surface area is the sum of the parts. Given the measurements of different prisms, pupils determine their surface areas. Individuals find the area of each surface and figure out the surface area by finding the sum. The video, part of a...

In this slope and area worksheet, students solve 2 short answer multi-step problems. Students determine the length of a wire given dimensions of a rectangle. Students find the slope of a line through a point on a curve.

Flip the triangles up and create a parallelogram. Using the idea of transformations, the video develops the area formula for rhombi and kites. The segment of an extensive geometry playlist uses the formula to find the areas of different...

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....

Using a slider, scholars build triangular numbers and their associated rectangles and use the geometric display to find the pattern to determine the next triangular number. They then relate that number to the area of the rectangle to...

Middle and high schoolers listen to a scenario about a puppy and use the scenario to develop formulas in order to find the area of a circle. In this circumference lesson, pupils understand how to find the radius, diameter, area of a...

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...

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...

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.

Use the area of polygons to calculate the area between curves. Pupils calculate areas under income and expense curves by filling the space with squares and right triangles. Using that information, they determine the profit related to the...