#I need help with b), I'm not sure what to do after using what I did in a).
fluid sinew
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main bobcat
Where is a in... well, a)?
main bobcat
What, exactly, did you prove in a)?
fluid sinew
So I'm unsure how to incorporate it
Proved that the Integral of f(x) borders 0 to a is equal to the integral of f(a-x) borders 0 to a
main bobcat
Right. Therefore... int(0, pi) f(x) = ?
fluid sinew
int (0, π) f(x) = int (0, π) f(π-x)
thats what i gathered, but when i acutally do it, idk what to do
main bobcat
Show me.
fluid sinew
unfortunately cannot take a photo rn, but i substituted every x to be π-x
from the original integral
main bobcat
Okay, so now the obvious question is, what's sin(pi - x)?
fluid sinew
just sin(x)
main bobcat
Prove it.
fluid sinew
sin(A-B) = sinAcosB - sinBcosA
= sinπcosx - sinxcosπ
= 0 • cosx - (-1)sin(x)
=sin(x)
main bobcat
Okay, then.
So then the only place where we retain (pi - x) is in the numerator, right?
main bobcat
That seems like a thing to try.
fluid sinew
nop dont think it worked
main bobcat
Why not?
fluid sinew
because so far, have not learned anything to simplify it i think
like i said i really do not know how to do it
main bobcat
...well, the integral of the sum is the sum of the integrals, right?
fluid sinew
right, so split it up?
fluid sinew
one of them can be solved using int f'(x)/f(x) = ln f(x)?
main bobcat
...okay, can you show your work on that one?
main bobcat
Right. And this is equal to the integral we had at the start, right?
fluid sinew
right so bring it to the right to become 2I
take t 2 over
then u sub
(or t sub since we were using dummy variables)
got it
is that right?
main bobcat
...what do you have now?
fluid sinew
basically the i answer i suppose
main bobcat
...okay then?
fluid sinew
+close