Find the exact length of the curve y=ln sec(x) from x=0 to x= pi/4
Find the area of the surface generated by revolving the curve 2*sqrt(x+3)
from x=1 to x=10 around the x axis
$\displaystyle \text{Length} = \int^{x=\frac{\pi}4}_{x=0} \sqrt{1+\left(\frac{dy}{dx}\right)^2} \, dx$
$\displaystyle \frac{dy}{dx} = \frac1{\sec x}\times \sec x\tan x = \tan x$
$\displaystyle \text{Length} = \int^{x=\frac{\pi}4}_{x=0}\sec x \, dx$
Can you continue now?