Question

Can you help me with this

Answer 1

Given:

`\begin{gathered} y=x+4 \\ y=x+2 \\ x=1 \\ x=4 \end{gathered}`

Required:

To find the volume of the solid by using washer method.

Step-by-step explanation:

Volume formula of Washer method is,

`V=\int_a^b\pi[(f(x)^2-g(x)^2]dx`

Therefore,

`\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[(4x^2)/(2)+12x]_1^4 \\ \\ =\pi[(64)/(2)+48-(4)/(2)-12] \\ \\ =\pi[32+48-2-12] \\ \\ =66\pi \end{gathered}`

Final Answer:

Volume is

`66\pi`