Originally Posted by

**deltemis** 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

then

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 $\displaystyle \Delta x$.

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 area of the strip, if so, how to properly do this? cause at some points the strip would be a rectangle but at some it'd be a triangle.