   Chapter 14.1, Problem 42E

Chapter
Section
Textbook Problem

Finding the Area of a Region In Exercises 37-42, use an iterated integral to find the area of the region bounded by the graphs of the equations. y = x ,     y = 2 x ,     x = 2

To determine

To calculate: The area bounded by the graphs of the equation given.

Explanation

Given:

The provided equation is y=x,y=2x,x=2.

Formula used: I=x=ax=by=cy=df(x,y)dydx

Calculation: Take the equations y=x,y=2x,x=2 into consideration. The points of intersection of these curves are (2,2),(2,4),(0,0). Now, draw the graph passing through these points. The region bounded by the graph of the equation y=x,y=2x,x=2 is as follows:

The area of the required region is given by Rdydx.

In this case, both curves pass through the origin, i.e., (0, 0).

Thus, it can be inferred that x changes from 0 to 2 and y changes from x to 2x within the bounded region

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