HE DID IT SO QUICKLY! Integral of sin^2(x)/cos^4(x)

Berkeley Math Tournament Integral Bee 11/2/24
#math #algebra #calculus #trig #數學 #cálculo #matemáticas

[xinpingdonohoe]

As soon as you see sec²(x)dx next to your function of tan(x), you're done.

[FilipeOliveira-mg]

to everyone in the comment section: yes it's an easy integral. Now try to do it in the same time it took you to write that comment

[potatadiggary]

As much as I don’t think it’s a hard integral, that guy finished it before I actually read the question

[nanamacapagal]

ATTEMPT:

Rewrite in terms of tan and sec.
INT(tan²x * sec²x dx)
Now substitute u = tanx,
INT(u² du)
= ⅓u³ + C
= ⅓tan³x + C

[erwanmonsi]

Easy peazy let A=int((sin^2 x/cos^4 x)dx)= int(tan^2 x * sec^2 x)dx but d(tan x)= sec^2 xdx hence A=int(tan^2 x)d(tanx)=1/3*tan^3 x + C

[ISuperI]

they finished before I processed the question

[JacobHernandez-ghcc]

This was one of my exam questions recently…

[devdroid]

I learned this in college 40 years ago, and now I have no idea of how I solved it.

[mwinmgl]

POV sitting here only knowing the power rule

[abdullahbashir]

We integrate the power of tan(x) and as we have its derivative sec^2(x) next to it

[ataishere]

i think it might've revolutionized the XOXO

[wickedprotos]

My calc professors Dr Passmore and Hall made us go to the board and do this. They were awesome.

[silverv]

Pro tip: Every time you see sin^n(x)/cos^m(x) try to separate it to tangent.

[SportsManVegetal]

If speed only comes from practice and lacks true intuition, it’s simply mechanical… almost anyone that has practiced as much as these two, could have done the same thing. Not impressive.

And yes, this is the perfect integral for simply memorizing. Soh Cah Toa

[blueslime]

Very easy, what age are these students?

[ice_wallow_come]

could you move cos^4x to the numerator making it cos^-4x then factor out cos^2x leaving you with just cos^-6x then just do a power rule?

[aadik]

Im such an idiot, i changed sin² to 1-cos²
Ill still be able to answer yeah but...

[adarshjha]

Took nearly 6 sec...while eating from one hand 😂

[길동아저씨]

im really sorry... but the something on grey pants omg.. sorry

[RealQinnMalloryu]

{sin^2+sin^2 ➖ }(x)^2/{cos^4+cos^4 ➖}(x)^2={sin^4+x^2 (cosx ➖ 2sinx+1).