1. ## "Washer" problem

Hi guys,

Was wondering if anyone can help with the following problem:

Find the volume of the solid genreated by revolving each region about the given axis.

Question: The region in the second quadrant bounded above the curve y = -x^3, below by the x-axis, and on the left by the line x = -1, about the line x = -2

Thank you

2. Hello, nmq3b!

Find the volume of the solid formed by revolving fhe region in quadrant 2,
bounded above the curve $y \,=\,-x^3$, below by the x-axis,
and on the left by the line $x = -1$, about the line $x = -2$
Code:
  :        *          |
:                   |
:         *         |
:         |*        |
:         |::*      |
:         |:::::*.  |
- + - - - - + - - - - * - - - - - -
-2        -1         |   *
:                   |      *
:                   |       *
|

"Shells" formula: . $V \;=\;2\pi\int^b_a\text{(radius)(height)}\,dx$

We have: . $\text{radius} = x + 2,\;\text{height} = -x^3$

Hence: . $V \;=\;2\pi\int^0_{\text{-}1}(x+2)(-x^3)\,dx \;=\;-2\pi\int^0_{\text{-}1}(x^4 + 2x^3)\,dx$