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anonymous
 one year ago
Integrate ((9sin^4(t) + 9cos^4(t))^1/2
anonymous
 one year ago
Integrate ((9sin^4(t) + 9cos^4(t))^1/2

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's all underneath the square root

Luigi0210
 one year ago
Best ResponseYou've already chosen the best response.5This right? \(\Large \int (\sqrt{9sin^4 t +9cos^4 t}) dt\)

Luigi0210
 one year ago
Best ResponseYou've already chosen the best response.5I would trying reducing it down, factor out that 9 first: \(\Large \int \sqrt{9(sin^4 t +cos^4 t}) dt \) Since 9 can come out of the square roots, you get this: \(\Large \int 3(\sqrt{sin^4 t +cos^4 t}) dt \) Make sense so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep got that down already  then I tried to use half angle identities but got stuck there

Luigi0210
 one year ago
Best ResponseYou've already chosen the best response.5You factored a square from each right?

Luigi0210
 one year ago
Best ResponseYou've already chosen the best response.5\(\Large 3\int (\sqrt{(sin^2 t )^2+(cos^2 t)^2} dt \) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep then used 1+cos(2t)/2 and 1cos(2t)/2

Luigi0210
 one year ago
Best ResponseYou've already chosen the best response.5But yea, what did you get after you tried that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Tried expanding them  but since its a square under square root can be factored out?

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.2i dont want to be killjoy but i think that integral dont have solution. its similar to:\[\int\limits_{}^{}\sqrt{a.\cos^{2}(x)+b.\sin ^{2}(x)} And this integral dont have solution neither.Its called the elliptic integral.

Luigi0210
 one year ago
Best ResponseYou've already chosen the best response.5Yea that's what I was getting too

Luigi0210
 one year ago
Best ResponseYou've already chosen the best response.5And your num lock is off or something there? :P

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am doing arc length it's from 0 to pi/2

Luigi0210
 one year ago
Best ResponseYou've already chosen the best response.5That would of been a bit helpful to know

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Answer in back says 3/2

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.2Maybe its a numerical solution or another way to calculate it, because you cant calculate it direclty with integrating methods.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0you should post or scan the question it looks like an arc lngth, but why guess? :p

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1might help to post the actual question ... or scan yeah

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok will try to write it out am on my iPad so here it goes Find the length of the following r(t) = <cos^3(t), sin^3(t)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So found derivative and then did magnitude and got to where the question is now !! :)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1what techniques have you covered?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I had thought to use the half angle formula to then take integral of ! In class covered take r'(t) then magnitude of r'(t) then take integral

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.2i think you have derivated wrong, check it again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Cos^3(t) = 3sin^2(t) Sin^3(t) = 3cos^2(t)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1im thinking .. and it may not be any better y = sin^3(acos(cbrt(x))) to eliminate the parameter maybe?

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.2you are forgeting chain rule

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1accursed chain rule lol

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1writing it as say: (cos(t))^3 might make it easier to recall chaining it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then what is it !? There is nothing with the t to do chain rule

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1if u = cos(t) u^3 derives to 3u^2 u'

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.2\[(\cos ^{3}(x))\prime=3.\cos ^{2}(x).(\sin(x))\]

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.2same with the sine

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So sine = 3sin^2(t)cos(t)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Gosh dang chain rule lol

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.2yep, it was a calculation mistake lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow lol such stupid mistake lol
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