Approximating Areas, The Definite Integral V3ax 6x4 1. Suppose f(x) a) Prove that f is increasing on the interval [0, 1]. b) Write down a finite sum which will be within 10-10 of the true value of the area enclosed by the x-axis, y = f(x), and x 1. You are not asked to actually compute the sum, just des cribe it in any convenient fashion. Hint: Your reasoning and your explanation may be guided by the picture be- low. Note that the horizont al and vertical axes have different scales. The shaded rectangles represent the difference between right- and left-endpoint approxima- tions. 1 3 у 2 1 What's the 1 X width? 2. Given that sin x dx of sin x and the rules of the definite integral, find the following definite integrals 1, and basing your conclusions only on the graph 1 a. Jo sin x dar, sin x dx, sin T da, b. с. d. sin x dx, e. J sin r dr 1
Approximating Areas, The Definite Integral V3ax 6x4 1. Suppose f(x) a) Prove that f is increasing on the interval [0, 1]. b) Write down a finite sum which will be within 10-10 of the true value of the area enclosed by the x-axis, y = f(x), and x 1. You are not asked to actually compute the sum, just des cribe it in any convenient fashion. Hint: Your reasoning and your explanation may be guided by the picture be- low. Note that the horizont al and vertical axes have different scales. The shaded rectangles represent the difference between right- and left-endpoint approxima- tions. 1 3 у 2 1 What's the 1 X width? 2. Given that sin x dx of sin x and the rules of the definite integral, find the following definite integrals 1, and basing your conclusions only on the graph 1 a. Jo sin x dar, sin x dx, sin T da, b. с. d. sin x dx, e. J sin r dr 1
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 9P: A soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can,...
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