# 4u integration qn (1 Viewer)

#### Masaken

##### Unknown Member

i'm a little stuck with this one, i feel like it's a lot easier than i think it is and i may be overthinking but
what i've done - did the reflection property (the q asked me to use it), so u also get I = integral ln(cosx), then you add them together and simplify to get 2I = integral ln(sin2x) dx - (pi/2)ln2.
not sure what to do from there, though? no idea how to proceed, some nudges in the right direction would be great though

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#### synthesisFR

##### Well-Known Member
what i've done - did the reflection property (the q asked me to use it), so u also get I = integral ln(cosx), then you add them together and simplify to get 2I = integral ln(sin2x) - (pi/2)ln2.
wdym by this

u could legit just use by parts tho...

#### synthesisFR

##### Well-Known Member
wait i think im thinking of sin(lnx)

lemme try the q now

#### synthesisFR

##### Well-Known Member
act yeah i think u have to use whatever the q told u to use
except i have no idea what u mean by reflection property

#### Masaken

##### Unknown Member
act yeah i think u have to use whatever the q told u to use
except i have no idea what u mean by reflection property
oh whoops
idk if it has another name but i learnt that it was called the reflection property

^ this property (ignore the graph i couldn't find another picture that had it)
basically the q asked use that property to integrate

#### synthesisFR

##### Well-Known Member
i didnt know it has a name lolz

#### howcanibesmarter

##### Well-Known Member
u still need help?

#### Masaken

##### Unknown Member
u still need help?
any help is appreciated from anyone pls I am very stuck

#### synthesisFR

##### Well-Known Member
oh mad days this is ugly

#### synthesisFR

##### Well-Known Member

is this right or did i do stupid mistake
just collect the 4 I's and then like evaluate that thing
im dying trying to write an english essay again so i need to kinad do that : P

#### howcanibesmarter

##### Well-Known Member
okie give me a sec i need to finish phys

#### howcanibesmarter

##### Well-Known Member
i used desmos for one part lol cus i got stuck too, managed to get an answer tho, idk if its right cus i plugged into integral calculator and it gave me smthing completely different...

Here is the integral calculator solution, (i don tthink this is it)

(sorry the back side of was my essay, apologies if its hard to read )

#### synthesisFR

##### Well-Known Member
i used desmos for one part lol cus i got stuck too, managed to get an answer tho, idk if its right cus i plugged into integral calculator and it gave me smthing completely different...

Here is the integral calculator solution, (i don tthink this is it)
View attachment 38937
(sorry the back side of was my essay, apologies if its hard to read )
wtf is this.. wth is Li and why is there An "i"

#### Masaken

##### Unknown Member
View attachment 38935

is this right or did i do stupid mistake
just collect the 4 I's and then like evaluate that thing
im dying trying to write an english essay again so i need to kinad do that : P
yeah I got up to the 2I bit but then our working out from there is different (cos I simplified it to 1/2sin2x, I'll check again and correlate my answers once I get back to my book after doing smth
thanks for the help tho

#### Trebla

Hint: Split the definite integral of ln(sin 2x)

#### Masaken

##### Unknown Member
i used desmos for one part lol cus i got stuck too, managed to get an answer tho, idk if its right cus i plugged into integral calculator and it gave me smthing completely different...
View attachment 38936
Here is the integral calculator solution, (i don tthink this is it)
View attachment 38937
(sorry the back side of was my essay, apologies if its hard to read )
not the essay
yeah I also got up to where u were at, I'm not sure where to go from there but -pi/2(ln2) is the right answer, ty for the help tho

#### synthesisFR

##### Well-Known Member
View attachment 38935

is this right or did i do stupid mistake
just collect the 4 I's and then like evaluate that thing
im dying trying to write an english essay again so i need to kinad do that : P
yeah I got up to the 2I bit but then our working out from there is different (cos I simplified it to 1/2sin2x, I'll check again and correlate my answers once I get back to my book after doing smth
thanks for the help tho
wait no i messed up with the integral with the cot x instead of 2x

but its still not working cuz u cant evaluate that so im not sure where ii went wrong?

#### howcanibesmarter

##### Well-Known Member
but its still not working cuz u cant evaluate that so im not sure where ii went wrong?
check ur 2nd integration by parts again ,it was cot2x, but it changed to cotx