MHB Find the volume by using shell and disk method

[jaychay]

Can you check it for me that I done it right or not ?
Thank you in advance.

 

[skeeter]

shells ...

$\displaystyle V = 2\pi \int_0^1 (x+2) \cdot x \, dx + 2\pi \int_1^4 (x+2) \cdot \sqrt{x} \, dx$

washers ...

$\displaystyle V = \pi \int_0^1 6^2 - (y+2)^2 \, dy + \pi \int_1^2 6^2 - (y^2+2)^2 \,dy$