Homework problem I recently got:
Find the length of the curve of $y=\sqrt{a^2-x^2}$ from $x=-2$ to $x=1$. Also find the area of the surface of revolution about the $x$-axis.
Having trouble understanding this. I'm not even sure what it would look like. I assume a is supposed to be a constant. Is it just a semi-circle with radius $a$. $X$-intercepts of $(-a,0)$ and $(a,0)$ and a max at $(0,a)$?
I'm a little iffy about how to first find the length.
I do know that I should start with $\int_{-2}^{1} 2\pi y ds$ since I am revolving about the x-axis.
Thanks for anyone who can help me out.