The volume of the solid formed by revolving the region about the x-axis is 2/45π.
Given:
Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis.
y = x^4, y = x^7
In addition, we must identify if the axis of revolution is vertical or horizontal.
In this case, the axis of revolution is on the x-axis, when y=0
The axis of revolution is Horizontal.
Select the method to find the volume. We select the Washer Method:
[tex]V = pi*\int\limits^b_a {(R(x))^2-(r(x))^2} \, dx[/tex]
From the image uploaded:
r(x) = x^7
R(x) = x^4
a = 0
b = 1
[tex]V = pi*\int\limits^1_0 {(x^4)^2-(x^7)^2} \, dx[/tex]
[tex]V = pi*\int\limits^1_0 {(x^8)-(x^{14})} \, dx[/tex]
[tex]V=pi*[(-1/15(1)^{15}+1/9(1)^9)-(-1/15(0)^{15}+1/9(0)^9)][/tex]
[tex]V = pi*[(2/45) - (0)][/tex]
V = 2/45*π
Learn more about the volume here:
https://brainly.com/question/1578538
#SPJ4
