Explain geometrically how the Midpoint Rule is used to approximate a definite integral.
SOLUTIONStep 1In midpoint formula we divide the interval [a,b] into n subintervals of equal width.Therefore we get We shall denote each of the subintervals as Where For each interval let .we then draw the graph for each subinterval with a height of Let us consider a graph with n=6. ApproxDef_G1 We can easily find the area for each of these rectangles using the formula .And therefore for a general we get that Thus the midpoint rule is used to approximate a definite integral.
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
The full step-by-step solution to problem: 2E from chapter: 7.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: approximate, Definite, explain, geometrically, integral. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 2E from 7.6 chapter was answered, more than 370 students have viewed the full step-by-step answer. The answer to “Explain geometrically how the Midpoint Rule is used to approximate a definite integral.” is broken down into a number of easy to follow steps, and 13 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.