   Chapter 5.1, Problem 4E

Chapter
Section
Textbook Problem

# Find the area of the shaded region. To determine

To find:

The area of the shaded region

Explanation

1) Concept:

The area A of the region bounded by the curves x=f(y), x=g(y) and the lines y=a and y=b, where f and g are continuous and f(y) g(y) for all y in a, b is

A= abfy-gydy

2) Given:

3) Calculation:

From the given graph,

we have that x=2y-y2 is the right boundary curve and x=y2-4y   is the left boundary curve.

Let,  fy=2y-y2 and gy=y2-4y

The shaded region lies between y=0 to y=3

Formula-

Area  A= abfy

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