Area of a curve calculus
[DOC File]Section 1
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Area problem – find the area under the curve (and the x-axis) between two endpoints. Area – is the limit (as n approaches infinity) of the sum of n rectangles. Distance problem – find the area under the velocity curve (and the x-axis) between two endpoints. Example 1: Sketch the graph and use geometry to find the area: A) B) Key Concept:
[DOC File]Unit 8: Area Between Curves and Applications of Integration
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Area Between Two Curves . Learning Objectives . A student will be able to: Compute the area between two curves with respect to the and axes. In the last chapter, we introduced the definite integral to find the area between a curve and the axis over an interval In this lesson, we will show how to calculate the area between two curves.
[DOC File]Equations and Graphs
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We now consider the second situation that arises in Calculus, the central problem of finding the area under the curve of a function . Area Under a Curve. First let’s describe what we mean when we refer to the area under a curve. Let’s reconsider our basic quadratic function Suppose we are interested in finding the area under the curve from to
[DOC File]Draft copy
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(The Monte Carlo method for estimating area under curve) Summary: Initially, students will graph a curve whose area can be found using Geometry methods using the Monte Carlo method that uses random points and probability to estimate the area under the curve. Students also calculate the area geometrically to prove that the method provides a reasonable estimate of area.
[DOC File]New Chapter 3
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Since this is an overestimate, the area under the curve is less then 10.14 units. We can also approximate the area under the curve using left endpoint rectangles as shown in figure 9.4. This approximation will give us an underestimate because the rectangles do not fill the entire area under the curve. (Figure 9.5
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