Can someone please help me with problem 3:
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).
Can someone please help me with problem 3:
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) $\displaystyle R = \int_{-1}^1 1 - x^2 \, dx$
b) each cross section has area = $\displaystyle 4x^2 = 4y$
volume of a square-sided cross section is $\displaystyle dV = 4y \cdot dy$
$\displaystyle
V = \int_0^1 4y \, dy
$
c) area of an equilateral triangle of side $\displaystyle s$ is $\displaystyle \frac{\sqrt{3}}{4}s^2$
$\displaystyle s = 2x $
$\displaystyle
V = \frac{\sqrt{3}}{4} \int_0^1 4y \, dy
$