![]() The exact area under f( x) = x 2 between x = 0 and x = 2 isįunction in the Math menu of the Graph screen using a x windowįind the area under the curve f( x) = x 2 between x = 0 and x = 3 and the area between x = 0 and x = 4.Įxamine the pattern of the areas as the interval becomes larger.ġ6.1.1 Predict the area under the curve f( x) = x 2 between x = 0 and x = 5 then use your calculator to check your prediction.ġ6.1.2 Find an algebraic formula that generalizes the area under the curve f( x) = x 2 between x = 0 and x = b by evaluating Take the limit of the function rrs to find the exact area under the curve between x = 0 and x = 2 ![]() The exact area under the curve was found by taking the limit of rrs as the number of rectangles approached infinity.įind the area under the curve f( x) = x 2 between x = 0 and x = 2. Notice that we have factored the constant w from the sum of terms. The function r r s was used to approximate the area of the region under the graph of f( x) and above the x-axis between x = a and x = b. In the previous module you found the area of the region bounded by the graph of f( x) = x 2, the vertical line x = 1, and the x-axis by using Riemann sums.Īs a review, the procedures and TI-89 functions used to find approximate and exact areas are listed below. ![]() You will extend your finding to find the relationship between an area function and its corresponding curve function. You will be asked to find specific area functions by using the programs rrs and lrs, which were developed in Module 15. ![]() ![]() Lesson 16.1: Area Functions, A Symbolic Approach In this lesson you will find functions that represent area under a curve using a symbolic approach. ![]()
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