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Dido525
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}^{}3\sin^2(t)\cos^4(t)dt\]

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0My work: \[3\int\limits_{}^{}\sin^2(x)\cos^4(t)dt\] \[3\int\limits_{}^{}\sin^2(t)\cos^2(t)\cos^2(t)dt\] \[3\int\limits_{}^{}\frac{ 1 }{ 2 }(1\cos(2t))(\frac{ 1 }{ 2 }(1+\cos(2t)))^2dt\] \[\frac{ 3 }{ 8 }\int\limits_{}^{}(1\cos(2t))((1+\cos(2t)))^2dx\] \[\frac{ 3 }{ 8 }\int\limits_{}^{}((\cos^3(2t)+\cos^2(2t)+\cos(2t)+1) dt\] \[\frac{ 3 }{ 8 }\int\limits_{}^{}((cos^2(2t))(cos(2t))+\cos^2(2t)+\cos(2t)+1))dt\] \[\frac{ 3 }{ 8 }\int\limits_{}^{}(\cos^3(2t)+\cos^2(2t)+\cos(2t)+1)dt\]

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0I don't know what to do after :( .

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0The 4th step should be a dt.

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1look in the back of your book at the "reduction" formula i think you can make a u sub earlier on though. maybe i am wrong

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Is there no other way?

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0I mean I did get a little further.

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 3 }{ 8 }\int\limits\limits_{}^{}(\cos^2(2t)\cos(2t)+\cos^2(2t)+\cos(2t)+1)dt\]

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1i would start with \[\int\cos^4(x)dx\int\cos^6(x)dx\] and then look in the back of the book

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 3 }{ 8 }\int\limits\limits\limits_{}^{}((1\sin^2(t)\cos(2t)+\cos^2(2t)+\cos(2t)+1)dt\]

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Where did that come from?

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1there are fomulas that i cannot remember for integrating \(\sin^n(x)\) and \(\cos^n(x)\) and i garantee you they are on the back cover of your text

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I know. I turn them into the half angles, which I did.

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0That stupid cos^2(2t) is getting in the way.

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1\(\sin^2(x)=1\cos^2(x)\) then multiply out it is easier than reinventing the wheel you are trying to derive the formula, (which is admirable) but it is easier to look it up

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Using another half angle won't help because they are multiplied together which just makes it squared afain,

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1why i find this topic rather dull. almost everything you need is printed on the back cover of your text

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0I know. I have to do it though.

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1then i really recommend looking up the formula for \(\int\cos^n(x)dx\)

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0So I get:\[\frac{ 3 }{ 8 }\int\limits_{}^{}(1\sin^2(2t))\cos(2t)+(1\sin^2(2t)+\cos(2t)+1)dt\]

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Can I ask a dumb question?

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0We have that constant out in front. If we break up the intergal into seperate sums do I distribute that constant to all the intergals?

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1sure so i can seem dumber if i cannot answer it

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1ignore the annoying 3, put it in at the end

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Hehe. Thanks. This should be easy now.

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1here it is \[\int\cos^n(x)dx = \frac{1}{n}\cos(x)\sin(x)+\frac{n1}{n}\int \cos^{n2}(x)dx\] use with \(n=4\) and again with \(n=6\)

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Ohh that's MASSIVELY convenient.

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1it is going to be a pain, but much less of a pain than what you were doing

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1\[\sin^2(x)\cos^4(x)=(1\cos^2(x))\cos^4(x)=\cos^4(x)\cos^6(x)\]
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