# Math Help - integration problems

1. ## integration problems

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

2. Originally Posted by samdmansam
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
$\text{Length} = \int^{x=\frac{\pi}4}_{x=0} \sqrt{1+\left(\frac{dy}{dx}\right)^2} \, dx$

$\frac{dy}{dx} = \frac1{\sec x}\times \sec x\tan x = \tan x$

$\text{Length} = \int^{x=\frac{\pi}4}_{x=0}\sec x \, dx$

Can you continue now?