# Math Help - Integrating Areas/Volumes

1. ## Integrating Areas/Volumes

http://www.math.rutgers.edu/~greenfi...dfstuff/w1.pdf

I can obviously sketch R and for the area, I just need to do a top minus bottom type deal, but I don't get parts b) and c).

2. Originally Posted by zhupolongjoe

http://www.math.rutgers.edu/~greenfi...dfstuff/w1.pdf

I can obviously sketch R and for the area, I just need to do a top minus bottom type deal, but I don't get parts b) and c).
a) $R = \int_{-1}^1 1 - x^2 \, dx$

b) each cross section has area = $4x^2 = 4y$

volume of a square-sided cross section is $dV = 4y \cdot dy$

$
V = \int_0^1 4y \, dy
$

c) area of an equilateral triangle of side $s$ is $\frac{\sqrt{3}}{4}s^2$

$s = 2x$

$
V = \frac{\sqrt{3}}{4} \int_0^1 4y \, dy
$