1. ## Surface Area (Calculus)

I'm getting confused on this problem, such as when to use dy and dx. If someone can please help me solve these problems and explain them, I would greatly appreciate it. Thank you.

Find the surface area generated by revolving the region bounded by the curve y = -x^2 + 5 and in the first quadrant about the
a) y-axis
b) x-axis
c) line x = -1

2. Originally Posted by turtle
I'm getting confused on this problem, such as when to use dy and dx. If someone can please help me solve these problems and explain them, I would greatly appreciate it. Thank you.

Find the surface area generated by revolving the region bounded by the curve y = -x^2 + 5 and in the first quadrant about the
a) y-axis
b) x-axis
c) line x = -1
The surface area rotating about the x-axis is given by:
$2\pi \int_a^b f(x)\sqrt{1+[f'(x)]^2}dx$
But the formula for rotating about the y-axis is not taught.
However is you really want to, you can think of:
$y=-x^2+5$
As, (rotate graph counterclickwise)
$x=-y^2+5$
Thus,
$y = \sqrt{5-x} \mbox{ on }[0,5]$