Question

solve the differential eq

Answer 1

dr/d0 = (sin(pi0))^4

Answer 2

0 = theata

Answer 3

lol integrals then suddenly diff eq lol =)) your curriculum makes me wonder

Answer 4

IT makes EVERYONE wonder.....

Answer 5

It's like they want to add them in to get us ready for diff eq later...

Answer 6

\[\frac{dr}{d\theta} = \sin^4 (\pi \theta)?\]

Answer 7

yessir.

Answer 8

\[dr = (\sin(\pi \theta))^4 d \theta\]

Answer 9

now take the integral of both sides

Answer 10

so it's time for half angle formula!

Answer 11

half angle?

Answer 12

i think this is just some trig sub thingy

Answer 13

Unless just do it normally...

Answer 14

\[\int \sin^4 (\pi \theta) d\theta\]
treat pii like a variable

Answer 15

i mean treat pi like a cosntant

Answer 16

I could say u = pi theta
du = pi dtheta

Answer 17

\[1/\pi \int\limits \sin^4(u) du\]

Answer 18

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 19

yup you're doing well

Answer 20

you cann integrate that though...

Answer 21

the integration of that is pretty long haha

Answer 22

I could do a half angle formula now :P

Answer 23

what half lol

Answer 24

\[1/2\pi \int\limits (1-\cos2u)^2 du\]

Answer 25

WE!

Answer 26

\[1/2\pi \int\limits (1-\cos2u) (1-\cos2u) du\]

Answer 27

\[1/2\pi \int\limits) (1-2\cos2u +( \cos2u)^2)du\]

Answer 28

:p

Answer 29

ok I give up hahha.

Answer 30

lol =)) like i said this integration is long

Answer 31

just look at this :( http://www.wolframalpha.com/input/?i=int+sin%5E4+%28x%29dx

Answer 32

long isnt it

Answer 33

Power reduction formula, maybe?

Answer 34

maybe :P

Answer 35

\(\sin^4(x)=\frac{1}{8}\left(3-4\cos(2x)+\cos(4x)\right)\)

Answer 36

Wolfram is wrong! :P

Answer 37

Did you misunderstand?

I said your statement is false for all possibilities.

Answer 38

I'll try your answer, it said wolfram's was incorrect.

Answer 39

Cool I win.

Answer 40

@KonradZuse, I apologize if I made a comment earlier that offended you. Many of my rather crazy-sounding or outlandish statements are completely jokes. I had actually meant that original comment in a positive light--I was glad to see that you have taken interest in mathematics and enjoy it more than most people. I had said this to other users on OS and complimented you during conversations with them.

Nonetheless, I apologize if my message came off completely contrary to how it was intended. I hope you'll forgive me.

P.S. My original comment was also a joke on Paul Erdos. Once again, nothing mean was meant.

Thanks,
Limitless