   Chapter 4.4, Problem 44E

Chapter
Section
Textbook Problem

Finding the Area of a Region In Exercises 41-46, find the area of the region bounded by the graphs of the equations. y = 2 x − x ,       y = 0

To determine

To calculate: The area of the region formed between the curves y=2xx and y=0.

Explanation

Given:

The two curves y=2xx and y=0.

Formula Used:

The following integration formula holds:

xkdx=xk+1k+1+c

Calculation:

The provided expression has 2 roots as 0 and 4.

Between the two roots, the function has a positive value. This can be checked using a test value of 2.

y(2)=222=2(21)>0

This implies that between 0 and 4, the curve y=2xx would lie above the x-axis or the line y=0

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