anonymous
  • anonymous
integrate sin^43x dx
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[\int\limits \sin^{43}(x) dx= - \cos^{43}(x)\] honestly, this is a weird question lol, so I'm not sure? ._.
anonymous
  • anonymous
+ C ofcourse
anonymous
  • anonymous
sstar, i don't know the answer but i'm almost sure that's not correct ><

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
LOL >_< I know, it looks weird
anonymous
  • anonymous
hmm, is it possible to let u = 43? I've never solved such thing lol
anonymous
  • anonymous
meh... no...this method is funny lol
anonymous
  • anonymous
sstarica the question is\[\int\limits \sin ^{4}3x dx\]
anonymous
  • anonymous
no, you have to substitute (cos x)^2 = 1 - (sin x)^2
anonymous
  • anonymous
oh that makes everything a lot better.... oneprince USE PARENTHESIS!
anonymous
  • anonymous
ok chia
anonymous
  • anonymous
no wait a min, isn't the sin to the power of 43?
anonymous
  • anonymous
chia.. solve it
anonymous
  • anonymous
was it to the power of 43? or to the power of 2? lol
anonymous
  • anonymous
give me a sec
anonymous
  • anonymous
it's sin(3x)^4
anonymous
  • anonymous
that's the question?
anonymous
  • anonymous
oh lol
anonymous
  • anonymous
ugh...sub 3x for u and then use the half angle formula to get cosine and sine together, integrate
anonymous
  • anonymous
sstar are you writing it out? caz i don't really want to...
anonymous
  • anonymous
>_< nvm, proceed chia, I misunderstood the question lol
anonymous
  • anonymous
oneprince, did you read what i wrote? is that enough?
anonymous
  • anonymous
AMISTRE! you can do this! ^_^
amistre64
  • amistre64
Howdy :)
anonymous
  • anonymous
lol
anonymous
  • anonymous
my brain is defunctioning, so I don't think I can write it down even though I took it this semester and it looks SIMPLE! would you amistre? ^_^
amistre64
  • amistre64
[S] sin^4(3x) dx this is missing something lol this came from something similar to -cos^5(3x) so what do we get when we derive that? and itll tell us what to add...
anonymous
  • anonymous
it's not really missing something, you can let u = 3x and solve normally like chia said
anonymous
  • anonymous
if only I remember lol >_<
amistre64
  • amistre64
Dx(-cos^5(3x)) = 5(3) sin^4(3x) which would be easy to solve right? So we need a "15" in front of your integral to convert it
amistre64
  • amistre64
lets multiply your original problem by "1"; or rather a convenient for of "1" such as 15/15..
anonymous
  • anonymous
where did you get cos^5?
amistre64
  • amistre64
then we can pull out the bottom "15" and integrate the rest up like normal
amistre64
  • amistre64
sin^4 comes from cos^5; or at least a version of it right?
anonymous
  • anonymous
you can do this : \[\int\limits (1-\cos^2(3x))^2 dx = \int\limits(1-2\cos^2u+\cos^2u)du\] and simply solve, right?
anonymous
  • anonymous
where u = 3x ? :)
anonymous
  • anonymous
right? .-.
anonymous
  • anonymous
isn't it simpler that way, lol?
amistre64
  • amistre64
\[\int\limits_{} \frac{5(3)}{5(3)} \sin^4 (3x) dx\]
anonymous
  • anonymous
why?
anonymous
  • anonymous
amistre, i think you're doing it wrong.. and i feel bad caz i'm not actually doing it...
amistre64
  • amistre64
\[\frac{1}{15} \int\limits_{} 5(3) \sin^4 (3x) dx\]
amistre64
  • amistre64
-cos^5 (3x)/15 + C
anonymous
  • anonymous
use the half angle formula to integrate sin or cos with a power you MUST have sin * cos
anonymous
  • anonymous
no, amistre, that's definitely wrong T-T
anonymous
  • anonymous
Why don't you make a substitution of \[u=3x \rightarrow dx = \frac{du}{3}\]so that then\[I=\frac{1}{3}\int\limits_{}{}\sin^4 u du\]and now use a reduction formula?
amistre64
  • amistre64
derive it back again, its right.... it should be right lol
anonymous
  • anonymous
using the way I cut it down, you'll get : \[= \int\limits1 du - 2\int\limits \cos^2u du + \int\limits \cos^2u du\] then you'll use for cos^2 u = 1/2(1+cos2u)
anonymous
  • anonymous
star is right
anonymous
  • anonymous
^_^ there, I hope it's right
anonymous
  • anonymous
as simple as that :)
anonymous
  • anonymous
sstar is completely right though i have a question where's the person who ASKED this question
anonymous
  • anonymous
LOL! watching us, hey oneprince did you understand what we did? ^_^
anonymous
  • anonymous
wait...he left ._.
anonymous
  • anonymous
yeah -_- but you got it sstar i have integrating cosine sins T-T so messy...
anonymous
  • anonymous
\[I=\frac{1}{3}(\frac{1}{32} (12 u-8 \sin(2 u)+\sin(4 u))+c)\]where u = 3x.
anonymous
  • anonymous
o_o....no wait O_O!
anonymous
  • anonymous
that's the final answer?
anonymous
  • anonymous
Sub. u=3x, then du = 3dx --> dx = du/3. Then you have 1/3*int[(sin^4(u) du]
anonymous
  • anonymous
You can use a reduction formula on sin^4(u)...
anonymous
  • anonymous
no need for reduction formula ^_^ + i got you lol :)
amistre64
  • amistre64
what happens when we derive:\[- \frac{\cos^5 (3x)}{15} + C\] ??
anonymous
  • anonymous
why do you want to derive it? that's not the answer lol? ._.
anonymous
  • anonymous
He wants to see if it matches the integrand.
anonymous
  • anonymous
oh
amistre64
  • amistre64
lol.... if its not the answer, then what does it derive to?
anonymous
  • anonymous
there's only one way to find out, T.R.Y ^_^
anonymous
  • anonymous
give me a sec, i'll do it
anonymous
  • anonymous
I won't even try since my page is lagging BADLY
anonymous
  • anonymous
anyhow, I'm off to review for my DM test tomorrow, good luck all ^_^
anonymous
  • anonymous
225 cos(3x)*sin(3x)^4
anonymous
  • anonymous
Omg, I gave you the answer ^^
anonymous
  • anonymous
wait i lied! i did * 15 instead of / 15 give me another min :P
anonymous
  • anonymous
what answer ._.
anonymous
  • anonymous
ohh i see why you put that 15 there it's cos(3x)*sin(3x)^4
anonymous
  • anonymous
cheers :D
anonymous
  • anonymous
Aren't you trying to find the integral of sin^4(3x)?
anonymous
  • anonymous
yeah but amistre is trying to show that he's right but i showed that he's wrong ^^
amistre64
  • amistre64
lol...not trying to show that im right, just trying to figure out what I did wrong :)
anonymous
  • anonymous
:x sorry i didn't mean it like that but do you get it now?
amistre64
  • amistre64
I see where my error cropped up ;)
anonymous
  • anonymous
lols kewls

Looking for something else?

Not the answer you are looking for? Search for more explanations.