Question

Please anyone answer me

Answer 1

Let's divide the shaded region into two areas:

area 1: x = 0 ---> x = 2

ares 2: x = 2 ---> x = 4

In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.

Area 1:

`A\frac{}{1} = ∫g(x)dx = ∫xdx = (1)/(2) {x}^(2) | (2)/(0) = 2`

Area 2:

`A\frac{}{2} = ∫(g(x) - f(x))dx`

`= ∫(x - {(x - 2)}^(2) )dx`

`= ∫( - {x}^(2) + 5x - 4)dx`

`= ( - (1)/(3){x}^(3) + (5)/(2) {x}^(2) - 4x) | (4)/(2)`

`= 2.67 - ( - 0.67) = 3.34`

Therefore, the area of the shaded portion of the graph is

A = A1 + A2 = 5.34