Integration year 2

[hasty raven]

They did this

i did this

i really hope this is clear

follow the arrows

<@&791435371564892232>

idk how im wrong

bytw i dint get to the end answer i was just trying to find the integral in terms of u

[hasty raven]

help?

[north sentinel]

This is where you loose it

You’ve converted back into theta and forgotten the original u sub

[gusty lotus]

yup this is how i did it for reference

much easier to keep in terms of u

[hasty raven]

wait but the arrow pointing to the right shows me putting it in the u sub form

like

-2u/1+u

[gusty lotus]

1+costheta=u

not 1+u

oj u did u=cosx

[hasty raven]

yeah i realised it would have been easier i did it the other way

but it was too late by then

so then when i looked over my working idk what i did wrong even if u = costheta

since technically more than 1 substitution should work and get to the same thing.

[north sentinel]

Even then you’d not be able to get to the right answer as you wouldn’t have the right bounds of integration

Bc you can’t do ln0

[hasty raven]

thats so weird so how would i know if it was wrong ?

since the only way you knew it was wrong

was because it was definite

if it was indefinite how would i know its wrong

[north sentinel]

I would probably always substitute the entire denominator / power etc. Just because you know it would be possible to get some lot of u to equal the entire thing