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# Rectangles beneath a curve A rectangle is constructed with ISBN: 9780321570567 2

## Solution for problem 22RE Chapter 4

Calculus: Early Transcendentals | 1st Edition

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Problem 22RE

Rectangles beneath a curve? A rectangle is constructed with one side on the positive ? x-axis. one side on the pos? itive ?y-axis, and the vertex opposite the origin on the curve y = cos x, for 0 < x < ?/2. Approximate the dimensions of the rectangle that maximize the area of the rectangle. What is the area?

Step-by-Step Solution:

Solution Step 1 In this problem a rectangle is constructed with one side on the positive x-axis and one side on the positive y-axis and the vertex opposite to the origin on the curve y = cos x, for 0 < x < /2. We have to find the dimensions of the rectangle that maximize the area of the rectangle. Step 2 Let the length of the rectangle be x and the breadth of the rectangle be y . Then the area of the rectangle is A = xy Given that the requirement of the rectangle lies on the curve of y = cos x, Therefore area A = x cos x To find the dimensions which increases the area, we have to find the x-derivative of A and equate it to 0. We have A = x cos x A(x) = cos x x sin x Now equating it to 0 we get., cos x x sin x = 0 cos x = x sin x x = cos x sin x x = cot x By the above equation it is impossible to solve for x. so let us use the graph of xand cot xdrawn below

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##### ISBN: 9780321570567

The answer to “Rectangles beneath a curve? A rectangle is constructed with one side on the positive ? x-axis. one side on the pos? itive ?y-axis, and the vertex opposite the origin on the curve y = cos x, for 0 < x < ?/2. Approximate the dimensions of the rectangle that maximize the area of the rectangle. What is the area?” is broken down into a number of easy to follow steps, and 59 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 22RE from 4 chapter was answered, more than 313 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: rectangle, axis, SIDE, area, curve. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 22RE from chapter: 4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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