i cannot figure this out for the life of me
whats the antiderivative of |cosx - sinx|?
absolute value(sinx+cosx)
>>7708405
show work?
>>7708405
bullshit, look at the graph, how can the antiderivative be always positv?
>>7708424
idk but this was on my final today. it said to use substitution but i didn't know what to use for u
>>7708435
im not op but look at the graph, the funktion goes up and down so the antiderivative has to go from positive to negative
>>7708445
No, no it doesn't.
>>7708392
well first you should split it into a system of equations.
cosx-sinx when cosx-sinx>0
-(cosx-sinx) when cosx-sinx<0
This seems trivially obvious, but we can use the fact that sine is odd and cosine is even to change these. -sin(x)=sin(-x) and -cos(x)=cos(x). so our system of equations become
cosx-sinx for cosx>sinx
cosx+sinx for cosx<sinx
cosx>sinx over the interval (-3pi/4, pi/4)
and sinx>cosx over the interval (pi/4, 5pi/4)
So know lets take antiderivative:
sinx+cosx for -3pi/4<x<pi/4
sinx-cosx for pi/4<x<5pi/4
So this >>7708405 isn't exactly true, only true from -3pi/4 to pi/4.
>>7708424
But the line is always above the axis, so the anti derivative WILL always be positive.
>>7708405
Top meme
>>7708449
Wrong. -cos(x) =/= cos(x).
cos(-x) = cos(x)
>>7708445
That's for a derivative mate.
>>7708392
f(x) = sqrt( (sin(x) + cos(x) )^2 ) now differentiate f(x)
>>7708445
Gezus Christ...
>>7708445
>funktion
>up and down
>ANTIderivative
Good job
