Math 151 - Workshop 13 (Riemann sums) We turn now to the problem of finding area under a curve. Suppose we want to find the area between the curve f(x) = x² and the x-axis on the interval [0, 1], as shown to the right. There is a process for finding this area exactly (we'll get to that next), but to understand that process we're first going to start by approximating this area with rectangles. 0 1 1. We're going to approximate the area shown above with four rectangles, using a right endpoint approximation, also called a right Riemann sum. (a) Start by dividing the interval [0, 1] into four equal-width subintervals, each of which has a length of 1/4. The first subinterval is [0, 1]. Write the other three subintervals. (b) Next, give the right endpoint of each subinterval a name of the form an. For example, x₁ = 1. Now, assign the correct values to #2, #3, and 24. (c) Now, calculate f(x1), f(x2), f(x3), and f(x4).
Math 151 - Workshop 13 (Riemann sums) We turn now to the problem of finding area under a curve. Suppose we want to find the area between the curve f(x) = x² and the x-axis on the interval [0, 1], as shown to the right. There is a process for finding this area exactly (we'll get to that next), but to understand that process we're first going to start by approximating this area with rectangles. 0 1 1. We're going to approximate the area shown above with four rectangles, using a right endpoint approximation, also called a right Riemann sum. (a) Start by dividing the interval [0, 1] into four equal-width subintervals, each of which has a length of 1/4. The first subinterval is [0, 1]. Write the other three subintervals. (b) Next, give the right endpoint of each subinterval a name of the form an. For example, x₁ = 1. Now, assign the correct values to #2, #3, and 24. (c) Now, calculate f(x1), f(x2), f(x3), and f(x4).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 68E
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