About the Rules & Moderation category (Part 1)

Announcements Rules & Moderation
#8227

It was the integral of cos^2(x) from 0 to 2pi

1 Like
#8228

OH
ok I see what you mean

1 Like
#8229

that’s an evil integral trick tho thbthtbhtbthbth

1 Like
#8230

I should really memorize the power reduction formulas tbhtbhtbhtbhtbht
and all the other trig identities

#8231

Bounds of integration problem:

Consider the region D defined by the following inequaltiies:
x>=0
y>=0
z>=0
z<=1-x^4
x^4+y^2+z^2<=1

Write hte iterated integral of the enclosed volume wit hthe order of integration being y,x,z, hten y,z,x, then z,y,x, then compute the integral for f(x,y,z)=(x^4+z)/sqrt(1-x^4-z^2) with the order of your choice

This is NOT, like, a difficult problem in THEORY. But I spent the first half with the order of integration swapped up in my mind, and I was very tired, and visualisation is hard

2 Likes
#8232

I wasn’t expected to know the trick I just came u with it after

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#8233

He just expected me to have it memorised

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#8234

I only got the one for y,x,z before he Kicked me out of the exam

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#8235

nyaaaaaaa every time I see a math problem like this in here I go “I should remember how to do this” and get nerd-baited into reviewing it

2 Likes
#8236

whenever i see a math problem i remember that math was the one subject i was terrible at

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#8237

If you do a coordinate transform of x^4=a^2 it’s spherical which is nice I guess

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#8238

you know now that im listing the subjects in my head i think i was exclusively good at a few things

#8239

I’m trying to figure out how to do the first one thbthtbhtbt

I see y goes from 0 to 1
then x goes from 0 to 1 - y^2
then z goes from 0 to… min(1 - x^4, sqrt(1 - x ^ 4 - y^2))
is that last bound fine? am I supposed to see a way to remove the min?

#8240

APPARENTLY. They mean that y is the innermost integral and z is the outermost

2 Likes
#8241

z,y,x is the only one where you have to sum two integrals

1 Like
#8242

…oh

#8243

THIS IS STUPID!!! THIS IS DUMB AND STUPID!!!

#8244

I guess that makes sense in terms of “what you integrate first” but also nyaaaaaaaaaaaaaaaaaaa

#8245

feels ~arbitrary either way

#8246

Yeah it’s arbitrary!!! I thought I was cheating by doing it the way it was apparently INTENDED. I spent like thrity minutes staring at this paper

1 Like