iTeachChem•16mo ago

definite integral

Im using reciprocal property here but idk where im doing wring the ans is piLn2

iTeachChem Helper•9/17/24, 1:50 PM

@Apu

iTeachChem Helper•9/17/24, 1:50 PM

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RReal potato Im using reciprocal property here but idk where im doing wring the ans is piLn2

BlindSniper•9/17/24, 1:53 PM

did u reverse the sign twice?

SirLancelotDuLac•9/17/24, 2:03 PM

Umm...

SirLancelotDuLac•9/17/24, 2:03 PM

Why not substitute x=tan(theta)

SSirLancelotDuLac Why not substitute x=tan(theta)

SirLancelotDuLac•9/17/24, 2:04 PM

That will do the trick ig.

BBlindSniper did u reverse the sign twice?

Real potatoOP•9/17/24, 2:05 PM

Oh my bad

Real potatoOP•9/17/24, 2:05 PM

But even after that how come we’ll get ln2?

SSirLancelotDuLac Why not substitute x=tan(theta)

Real potatoOP•9/17/24, 2:06 PM

Oh yeah that would definitely work but im currently focused on learning this reciprocal thing

RReal potato Oh yeah that would definitely work but im currently focused on learning this rec...

SirLancelotDuLac•9/17/24, 2:14 PM

I see. Then notice that $f(x)+f(\frac{1}{x})=ln(x+\frac{1}{x})$, so $I=\int_{0}^{1} ln(x+\frac{1}{x}) ,dx$

TeXit•9/17/24, 2:14 PM

SirLancelotDuLac

RReal potato Im using reciprocal property here but idk where im doing wring the ans is piLn2

SirLancelotDuLac•9/17/24, 2:19 PM

Also you seem to have changed sign twice in 5th line of solving (one while intechanging limits and other inside the log.)

SSirLancelotDuLac Also you seem to have changed sign twice in 5th line of solving (one while intec...

Real potatoOP•9/17/24, 3:39 PM

After correction im getting this

Real potatoOP•9/17/24, 3:40 PM

Real potatoOP•9/17/24, 3:40 PM

,rotate

TeXit•9/17/24, 3:40 PM

TTeXit Click to see attachment

SirLancelotDuLac•9/18/24, 1:17 AM

Yep. This is correct, but the reciprocal thing becomes the question itself.

TTeXit **SirLancelotDuLac**

SirLancelotDuLac•9/18/24, 1:18 AM

Apart from tan(theta) sub., the other way is this ig.

Real potatoOP•9/19/24, 4:31 AM

Ah it seems to me that the tan(thetha) thing would work better here

RReal potato Ah it seems to me that the tan(thetha) thing would work better here

iTeachChem•9/28/24, 3:37 AM

intense!

iTeachChem•9/28/24, 3:37 AM

sorted?

Real potatoOP•9/28/24, 9:05 AM

Yup

Real potatoOP•9/28/24, 9:06 AM

+solved @SirLancelotDuLac

iTeachChem Helper•9/28/24, 9:06 AM

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