[ot][ot][ot][personal] whirligig small thoughts

[Undescribed Horrific Abuse, One Victim & Survivor of Many]

i think i did integral wrong. that it's not 3x^3 but rather 1/3 x^3 .
seems quite likely.

let's try to find via another route. ummmmmmmmmmmmm


thinking of the 1/2 in the triangle area, since we are trusting elsewhere.
is this related to 1/2 x^2 somewhere maybe? or 1/2 x?

the area of a triangle is integral of y(x) = slope * x
where slope = h/w
and integral is 0...w

so
integral(x * h / w, dx, 0...w) = 1/2 h * w
uhh
indefinite integral, assuming exponent goes to denominator
1/2 x^2 * h / w | x = w
1/2 w^2 * h / w = 1/2 w * h
so integration puts the _new_ exponent in the _denominator_. check
with calculating triangle area.