anonymous
  • anonymous
solve this integral :/ not sure how to do this!
Mathematics
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anonymous
  • anonymous
solve this integral :/ not sure how to do this!
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits_{} \sin^5 t \cos^4 t dt\]
Zale101
  • Zale101
|dw:1442984817219:dw|
Astrophysics
  • Astrophysics
Some general rules with these trig functions |dw:1442984972414:dw|

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Zale101
  • Zale101
Any ideas of what to do next?
Zale101
  • Zale101
That chart is very helpful! @astrophysics
Astrophysics
  • Astrophysics
Yeah, it's pretty awesome :P
Astrophysics
  • Astrophysics
http://puu.sh/kl22A/732d78a86f.png if anyone wants the link XD
anonymous
  • anonymous
sorry!! i am back!! :) i am reading the chart right now :) one sec!! hopefully i can have a clue what happens next:)
anonymous
  • anonymous
okay, i see now what you did @Zale101 so i strip one sin away and get|dw:1442985650253:dw|
anonymous
  • anonymous
not sure what to do next though :/
Astrophysics
  • Astrophysics
|dw:1442985664022:dw|
anonymous
  • anonymous
ohh so i would get this? |dw:1442985687508:dw|
Zale101
  • Zale101
|dw:1442985746191:dw|
anonymous
  • anonymous
okay!! i forget though, from here, do i sub something in? :/
Zale101
  • Zale101
U-Sub! :)
anonymous
  • anonymous
so we get integral sin t (sin^2 t)^2 u^4 dt ?
Zale101
  • Zale101
Nope. First of all, you cant have u while the rest of the terms are in t. Second, you have to use trig identities for (sin^2t)^2
anonymous
  • anonymous
ohhh how do i do that then?
Zale101
  • Zale101
\((sin^2t)^2=(1-cos^2t)^2\)
anonymous
  • anonymous
ohh the square thing?
Zale101
  • Zale101
\(sin^4t=(sin^2t)^2=(1−cos^2t)^2\)
anonymous
  • anonymous
confused which trig functions to insert in now?
Zale101
  • Zale101
Yes. If you wan to replace sin^2 with the trig identities 1-cos^2t. But sin is squared, so the identity has to be squared as well.
anonymous
  • anonymous
ohh but it is fine leaving like sin? what happens next?
Zale101
  • Zale101
Next, you do u-sub. But first show me your integral now after using trig identities.
anonymous
  • anonymous
\[\int\limits_{} (1-\cos^2 t)((1-\cos^2)^2 t)^2 cost^4 t dt\] this?
Zale101
  • Zale101
\[\int\limits_{}^{}\sin(t) (\sin^2(t))^2\cos^4(t)dt\] \[\int\limits_{}^{}\sin(t) (1-cos^2(t))^2\cos^4(t)dt\]
anonymous
  • anonymous
ohh okay oopsies :P what happens now? :O
Zale101
  • Zale101
What you did was wrong because you can replace sint with 1-cos^2 trig identities say \(sin^2t=1-cos^2\)
anonymous
  • anonymous
ohhhh:O
Zale101
  • Zale101
\(sin^2t+cos^2t=1\)
Zale101
  • Zale101
What is your next step now?
anonymous
  • anonymous
i integrate? :/
Zale101
  • Zale101
How?
anonymous
  • anonymous
i am not sure :(
anonymous
  • anonymous
i am sorry :( i am very bad at calc:(
Zale101
  • Zale101
We need u-sub here. What would be you u in this case?
Zale101
  • Zale101
your*
anonymous
  • anonymous
u=sin(t) ?
Zale101
  • Zale101
Would u=sint work?
anonymous
  • anonymous
i think so :/
Zale101
  • Zale101
I will try u=sint and see if it works.
anonymous
  • anonymous
ok!! sorry, i get very confused with these concepts :/
Zale101
  • Zale101
|dw:1442986993486:dw|
anonymous
  • anonymous
ohhh okay :/ what should we do then?
Zale101
  • Zale101
try u=cos(t)
Astrophysics
  • Astrophysics
A saying I remember, get the odd man out! You want the odd man out!
anonymous
  • anonymous
okay!! where do we sub that into ? :/
Zale101
  • Zale101
With integration, here is what you should do. Every time you make an educated guess on what might the u be, do the integration and see if it works.If not, then try something else. This is what i did with integral and it was helpful.
Zale101
  • Zale101
integral problems*
anonymous
  • anonymous
ohhh okie :) so we should use u=cos(t) and so we do this? \[\int\limits_{}sint(1-u)^2 u^4 dt \]
Zale101
  • Zale101
You cant place in the u when you have not finished u-subbing
anonymous
  • anonymous
ohh no! I'm sorry, i don't know what to do here :(
Astrophysics
  • Astrophysics
When you do a u sub, you must also get the derivative, that's what will cancel out the sint \[u= cost \implies du= - sint dt\]
Astrophysics
  • Astrophysics
You don't want t and u's, just one variable
anonymous
  • anonymous
okay! what would it look like then?
Zale101
  • Zale101
Do u=cost and du=-sint dt and tell me what you will get
anonymous
  • anonymous
i get this? is it correct? integral with plug in u and du udu and i sub in and replace and get this? -1/5cos^5t+2/7cost^7t-1/9cos^9t+C?
anonymous
  • anonymous
thank you so much @Zale101 @Astrophysics i will try to figure this one out some more tomorrow! i need to sleep now because it is 2am here and i have to be up in four and a half hrs!! thanks so much for your help!!! :D sorry it was hard for me to understand!! have a nice night!!
Zale101
  • Zale101
Alright, good luck and take care!
Astrophysics
  • Astrophysics
Good night! :)
Zale101
  • Zale101
Just a type error i made "What you did was wrong because you \(\color{red}{can't}\) replace sint with 1-cos^2"

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