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Dido525Best ResponseYou've already chosen the best response.0
\[\int\limits_{}^{}3\sin^2(t)\cos^4(t)dt\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
My work: \[3\int\limits_{}^{}\sin^2(x)\cos^4(t)dt\] \[3\int\limits_{}^{}\sin^2(t)\cos^2(t)\cos^2(t)dt\] \[3\int\limits_{}^{}\frac{ 1 }{ 2 }(1\cos(2t))(\frac{ 1 }{ 2 }(1+\cos(2t)))^2dt\] \[\frac{ 3 }{ 8 }\int\limits_{}^{}(1\cos(2t))((1+\cos(2t)))^2dx\] \[\frac{ 3 }{ 8 }\int\limits_{}^{}((\cos^3(2t)+\cos^2(2t)+\cos(2t)+1) dt\] \[\frac{ 3 }{ 8 }\int\limits_{}^{}((cos^2(2t))(cos(2t))+\cos^2(2t)+\cos(2t)+1))dt\] \[\frac{ 3 }{ 8 }\int\limits_{}^{}(\cos^3(2t)+\cos^2(2t)+\cos(2t)+1)dt\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
I don't know what to do after :( .
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
The 4th step should be a dt.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
look 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
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Is there no other way?
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
I mean I did get a little further.
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
\[\frac{ 3 }{ 8 }\int\limits\limits_{}^{}(\cos^2(2t)\cos(2t)+\cos^2(2t)+\cos(2t)+1)dt\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
i would start with \[\int\cos^4(x)dx\int\cos^6(x)dx\] and then look in the back of the book
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
\[\frac{ 3 }{ 8 }\int\limits\limits\limits_{}^{}((1\sin^2(t)\cos(2t)+\cos^2(2t)+\cos(2t)+1)dt\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Where did that come from?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
there 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
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Yeah, I know. I turn them into the half angles, which I did.
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
That stupid cos^2(2t) is getting in the way.
 one year ago

satellite73Best 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
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Using another half angle won't help because they are multiplied together which just makes it squared afain,
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
why i find this topic rather dull. almost everything you need is printed on the back cover of your text
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
I know. I have to do it though.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
then i really recommend looking up the formula for \(\int\cos^n(x)dx\)
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
So I get:\[\frac{ 3 }{ 8 }\int\limits_{}^{}(1\sin^2(2t))\cos(2t)+(1\sin^2(2t)+\cos(2t)+1)dt\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Can I ask a dumb question?
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
We have that constant out in front. If we break up the intergal into seperate sums do I distribute that constant to all the intergals?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
sure so i can seem dumber if i cannot answer it
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
ignore the annoying 3, put it in at the end
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Hehe. Thanks. This should be easy now.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
here 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 \(n=6\)
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Ohh that's MASSIVELY convenient.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
it is going to be a pain, but much less of a pain than what you were doing
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\[\sin^2(x)\cos^4(x)=(1\cos^2(x))\cos^4(x)=\cos^4(x)\cos^6(x)\]
 one year ago
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