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4u integration qn (1 Viewer)

Masaken

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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

thanks in advance
 
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synthesisFR

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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

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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

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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
1689074808666.png
^ this property (ignore the graph i couldn't find another picture that had it)
basically the q asked use that property to integrate
 

synthesisFR

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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

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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...
IMG_5863.jpg
Here is the integral calculator solution, (i don tthink this is it)
Screen Shot 2023-07-11 at 9.53.40 pm.png
(sorry the back side of was my essay, apologies if its hard to read )
 

synthesisFR

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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

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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
 

Masaken

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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

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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
IMG_2485.jpg
but its still not working cuz u cant evaluate that so im not sure where ii went wrong?
 

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