I
iTeachChem•10mo ago
the_nub

adv math

No description
21 Replies
iTeachChem Helper
iTeachChem Helper•10mo ago
@Apu @Apu
iTeachChem Helper
iTeachChem Helper•10mo ago
Note for OP
+solved @user to close the thread when your doubt is solved. Mention the user who helped you solve the doubt. This will be added to their stats.
iTeachChem Helper
iTeachChem Helper•10mo ago
Note for OP
+solved @user to close the thread when your doubt is solved. Mention the user who helped you solve the doubt. This will be added to their stats.
the_nub
the_nubOP•10mo ago
sorry pinged twice
ᴘɪᴄᴄʜɪ | 🎧 🎶
🤔 damn I'll check Hey! Did you click on the button once or twice?
Linarp
Linarp•10mo ago
hey have you tried smth by IBP?
the_nub
the_nubOP•10mo ago
twice if i remember correctly yeah, it was getting really lengthy. i did it like 2-3 times but im hitting dead ends .
TeXit
TeXit•10mo ago
Comrade Rock Astley
No description
Comrade Rock Astley
Comrade Rock Astley•10mo ago
Since the denominator is a definite integral let it be some k one sec I'll work on it Well there's a not so complicated method Expand sinx and cosx using Taylor series expansions You get this
Comrade Rock Astley
Comrade Rock Astley•10mo ago
No description
Comrade Rock Astley
Comrade Rock Astley•10mo ago
Here k is some infinitely large number You can now drop all terms except the one with the largest exponent This gives you
TeXit
TeXit•10mo ago
Comrade Rock Astley
No description
Comrade Rock Astley
Comrade Rock Astley•10mo ago
Now we can cancel the denominators after integration since they're practically equal So this reduces to 2/pi
TeXit
TeXit•10mo ago
Comrade Rock Astley
No description
Comrade Rock Astley
Comrade Rock Astley•10mo ago
so C=-1 so that r and k cancel out L = 2/pi answer is 3 now there's one thing left to explain...the reason I've used k+1 instead of k-1 or any other number in the denominator is so that we get the result, but...there's gotta be a logical reason for that We know sin^2x + cos^2x=1 for all x. Hence we note that sin^2x+cos^2x does not depend on x. Now the highest exponent in the terms of sin^2x here is x^2k. To cancel it we’ll need the terms in cos^2x formed by the multiplying x^k-1 and x^k+1 If x^k-1 is the largest term in cosx, it can be proven that there is always a positive term of x^2k in the expression sin^2x+cos^2x that won’t cancel out It won’t cancel out perfectly, but when all other terms are included they cancel out in the end and that’s why x^k+1 is used
Linarp
Linarp•10mo ago
Nice work @Comrade Rock Astley really well put solution
the_nub
the_nubOP•9mo ago
i kinda lost you on this step. are you saying to cancel out the x^r . x^k even when the denominator has an extra x in it? like can you explain how you took it from here
No description
TeXit
TeXit•9mo ago
No description
Comrade Rock Astley
Comrade Rock Astley•9mo ago
The denominators I’m talking about are the r+k+1 and r+k+2 you get after integrating yeah go on just integrate normally from here
the_nub
the_nubOP•9mo ago
oh okayy. thankss so much, it was actually a very comprehensive solution +solved @Comrade Rock Astley
iTeachChem Helper
iTeachChem Helper•9mo ago
Post locked and archived successfully!
Archived by
<@801817464425807892> (801817464425807892)
Time
<t:1714392765:R>
Solved by
<@769492044837552139> (769492044837552139)

Did you find this page helpful?