Integrals: Arc Length and hydrostatic force problem Alright my
first is to simply find the length of the curve of: y = ln(sec
x) from 0 to pi/4 the steps I have taken is the usual dy/dx =
tan x integral of sqrt(1 + (tan x)^2) from here is where I am
stuck. I've tried using u-substitution but then du would've been
more complicated to calculate out and I don't know how to
integrate the expression sqrt(1 + (tan x)^2). what should I
proceed with? my next problem is: a swimming pool 20ft wide,
40ft long, bottom is an inclined plane. shallow end is 3 ft
long, deep end is 9ft long and pool is full of water. find
hydrostatic force on one of the sides. I started by drawing a
picture of said pool then I made a plane with the x axes with
origin at top of pool going down then i make a strip of . this
is where I am stuck as I am not sure as to which side I should
be working towards finding pressure of (if it matters). how
should I proceed with this one? I'm looking at a few other
answers and I'm guessing I should find the