Currently I'm struggeling with a mechanics problem. My issue is not the mechanics, but the mathematics. Therefore I see it fit to post this question here.
I need to integrate along the axis of the beam and I need to do this in polor coordinates. This is where I get stuck. I know from calculus that I need to express the x and y value in an angle in combination with a geometric function.
It looks like this beam is the quarter of a circle. I think this piece of data is usefull, but I don't know how to proceed.
Question: How do I integrate along the axis of this beam in polor coordinates?
How do I use polar coördinates in order to integrate along a curved axis?
I've flipped your sketch left to right. Let $A=(a,0)$ and $B=(0,a).$ In polar coordinates, $x=a\cos \theta,$ $y=a\sin \theta$ and $\theta$ goes from $0$ to $\pi\over 2$ radians. For example, $$\int_0^{\pi/2} a\, d\theta$$ gives the length of your beam.