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anonymous
 one year ago
solve this integral :/ not sure how to do this!
anonymous
 one year ago
solve this integral :/ not sure how to do this!

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{} \sin^5 t \cos^4 t dt\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Some general rules with these trig functions dw:1442984972414:dw

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2Any ideas of what to do next?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2That chart is very helpful! @astrophysics

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Yeah, it's pretty awesome :P

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2http://puu.sh/kl22A/732d78a86f.png if anyone wants the link XD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry!! i am back!! :) i am reading the chart right now :) one sec!! hopefully i can have a clue what happens next:)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, i see now what you did @Zale101 so i strip one sin away and getdw:1442985650253:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure what to do next though :/

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2dw:1442985664022:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh so i would get this? dw:1442985687508:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay!! i forget though, from here, do i sub something in? :/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so we get integral sin t (sin^2 t)^2 u^4 dt ?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2Nope. 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
 one year ago
Best ResponseYou've already chosen the best response.0ohhh how do i do that then?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2\((sin^2t)^2=(1cos^2t)^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh the square thing?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2\(sin^4t=(sin^2t)^2=(1−cos^2t)^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0confused which trig functions to insert in now?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2Yes. If you wan to replace sin^2 with the trig identities 1cos^2t. But sin is squared, so the identity has to be squared as well.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh but it is fine leaving like sin? what happens next?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2Next, you do usub. But first show me your integral now after using trig identities.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{} (1\cos^2 t)((1\cos^2)^2 t)^2 cost^4 t dt\] this?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2\[\int\limits_{}^{}\sin(t) (\sin^2(t))^2\cos^4(t)dt\] \[\int\limits_{}^{}\sin(t) (1cos^2(t))^2\cos^4(t)dt\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh okay oopsies :P what happens now? :O

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2What you did was wrong because you can replace sint with 1cos^2 trig identities say \(sin^2t=1cos^2\)

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2What is your next step now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i am sorry :( i am very bad at calc:(

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2We need usub here. What would be you u in this case?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2I will try u=sint and see if it works.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok!! sorry, i get very confused with these concepts :/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh okay :/ what should we do then?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2A saying I remember, get the odd man out! You want the odd man out!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay!! where do we sub that into ? :/

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2With 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh okie :) so we should use u=cos(t) and so we do this? \[\int\limits_{}sint(1u)^2 u^4 dt \]

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2You cant place in the u when you have not finished usubbing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh no! I'm sorry, i don't know what to do here :(

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2When 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
 one year ago
Best ResponseYou've already chosen the best response.2You don't want t and u's, just one variable

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay! what would it look like then?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2Do u=cost and du=sint dt and tell me what you will get

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i 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^7t1/9cos^9t+C?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank 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
 one year ago
Best ResponseYou've already chosen the best response.2Alright, good luck and take care!

Zale101
 one year ago
Best ResponseYou've already chosen the best response.2Just a type error i made "What you did was wrong because you \(\color{red}{can't}\) replace sint with 1cos^2"
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