integrating sin^2 x (1 Viewer)

[akuchan]

integrate sin^2 x(degrees)
show all/most working out plz

 

[jemsta]

use double angle formula
cos2x=1-2sin^2x
2sin^2x=1-cos2x
sin^2x=1/2(1-cos2x)
then just integrate as usual from there

 

[nichhhole]

ok.
well u change it into sin^2x = 1/2 (1 -cos2x)

so...
sin^2x = 1/2 [integration symbol] 1 - cos 2x

= 1/2 [ x -(sin2x/2) ]

= x/2 - sin2x/4

 

[nichhhole]

jemmmmmmmmmmmmmsta

too fast.

 

[jb_nc]

You could use integration by parts too, couldn't you?

 

[jemsta]

haha assuming hes doing ext 2....but why make it any harder

 

[jb_nc]

haha assuming hes doing ext 2....by why make it any harder

lol

 

[nichhhole]

You could use integration by parts too, couldn't you?

haha yeah you probably could..
but i wouldnt do it unless they specifically asked for that method..

 

[elseany]

oooer nichole on the ball !

btw being pedantic here, but just incase you didnt realise you cant integrate anything in degrees, its not possible to use degrees with any form of calculus, its the reason why radians were invented.

and lol, im soo bored that i tried to do it with parts, you need two applications for it to come out.

 

[akuchan]

actually the actual question was integrate sin^2 x(degrees) lol
and that changes to 180/pi or something (guessing) and i get a slightly different final answer than the book =/

 

[SoulSearcher]

oooer nichole on the ball !

btw being pedantic here, but just incase you didnt realise you cant integrate anything in degrees, its not possible to use degrees with any form of calculus, its the reason why radians were invented.

and lol, im soo bored that i tried to do it with parts, you need two applications for it to come out.

Integration by parts for this question was fun enough to keep me occupied for a couple of minutes

 

[nichhhole]

actually the actual question was integrate sin^2 x(degrees) lol
and that changes to 180/pi or something (guessing) and i get a slightly different final answer than the book =/

ahh..
u dont know radians yet?
ok..
basic rundown.

180 degrees= pi

90 degrees = pi/2

60= pi /3

45 deg = pi/4

30deg = pi/6

and so on..
so it's just a fraction of piiiiiiii!

 

[SoulSearcher]

Multiply the degree by pi/180, then you can continue on from there :uhhuh: What is the answer btw?

 

[akuchan]

i do know radians lol sort of
answer is 1/2 (x - 90/pi sin (2x)degrees) + C ...=/

if i got sin pi/90 would that equal the sin 2x degrees and still be right

 

[SoulSearcher]

i do know radians lol sort of
answer is 1/2 (x - 90/pi sin (2x)degrees) + C ...=/

if i got sin pi/90 would that equal the sin 2x degrees and still be right

You wouldn't have got sin pi/90, but sin (x*pi/90), and when you multiply x*pi/90 by 180/pi to convert it back to degrees again, yes, you would get sin 2x(degrees).

 

[jemsta]

haha i got a feeling the integration by parts is going to be a lot more tedious
but then again, itll help if youre an ext 2 student

 

[jb_nc]

haha i got a feeling the integration by parts is going to be a lot more tedious
but then again, itll help if youre an ext 2 student

i had a go, got it wrong -- waiting until semester 2

 

[akuchan]

lol sin (x*pi/90) >.>" close enough i just got lazy hahah
anyway thanks for the help

i dont need to know any of this 'integration by parts' for ext 1 do i? "

 

[jb_nc]

nah

 

[jemsta]

haha yeah youre lucky
i think you need to know substitution only in ext 1...unless you do a maths subject in uni