Given:
[tex]\begin{gathered} y=x+4 \\ y=x+2 \\ x=1 \\ x=4 \end{gathered}[/tex]Required:
To find the volume of the solid by using washer method.
Explanation:
Volume formula of Washer method is,
[tex]V=\int_a^b\pi[(f(x)^2-g(x)^2]dx[/tex]Therefore,
[tex]\begin{gathered} V=\int_1^4\pi[(x+4)^2-(x+2)^2]dx \\ \\ =\int_1^4\pi[x^2+16+8x-x^2-4-4x]dx \\ \\ =\int_1^4\pi[4x+12]dx \\ \\ =\pi[\frac{4x^2}{2}+12x]_1^4 \\ \\ =\pi[\frac{64}{2}+48-\frac{4}{2}-12] \\ \\ =\pi[32+48-2-12] \\ \\ =66\pi \end{gathered}[/tex]Final Answer:
Volume is
[tex]66\pi[/tex]