Answer:
The volume of the solid is 19.[tex]\overline{142857}[/tex] unit³
Step-by-step explanation:
The given function is y = x³
The solid is created by revolving R about the line y = 1
We have that when y = 1, x = 1
Taking the end point as x = 2, we have the volume given by the washer method as follows;
[tex]V = \pi \cdot \int\limits^a_b {\left( [f(x)]^2 - [g(x)]^2 \right)} \, dx[/tex]
Where;
a = 1, and b = 2, we have;
g(x) = 1
[tex]V = \pi \cdot \int\limits^{2}_1 {\left( [x^3]^2 - [1]^2 \right)} \, dx = \pi \cdot \left[\dfrac{x^7}{7} + x \right]_1^{2} = \pi \cdot \left[\dfrac{2^7}{7} +2 -\left( \dfrac{1^7}{7} + 1\right)\right] =19\dfrac{1}{7}[/tex]
The volume of the solid, V = [tex]19\dfrac{1}{7}[/tex] unit³ = 19.[tex]\overline{142857}[/tex] unit³
