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anonymous
 5 years ago
in Substitution Rule
anonymous
 5 years ago
in Substitution Rule

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myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits\limits_{0}^{\frac{1}{2}}\frac{\sin^{1}(x)}{\sqrt{1x}} dx\]

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1i would make the substitution: x = sin^2(u) dx = 2sin*cos du \[\rightarrow 2\int\limits_{0}^{.5}u^{2} \sin(u) du\] Then use integration by parts

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but I don't know how to do it

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0Do you know integration by parts?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i do but that question is on substitution not in integration by parts

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0Why can't we do both?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}^{}u^2 \sin(u) du=u^2( \cos(u))\int\limits_{}^{}2u (\cos(u)) du\] you will need to do integration by parts one more time

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok Thank you a lot guys :)

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2one thing I am confused on here, where did we get u^2 ? are you saying arcsin(sin^2u)=u^2 ?

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1yes arcsin(sin u) = u by definition of the inverse function

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2somehow the idea that that extends to arcsin(sin^n(u))=u^n has never been brought to my attention. thanks

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0could we have just used the substitution:\[u = \sin^{1}(x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ah disregard, i didnt look at the denominator properly.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i don't know if that is true turing

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2arcsin(sin(u^n))=u^n arcsin(sin^n(u))=?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i agree with the first equation you have turing

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1wait now that i look at it again, i think i have it backwards. sorry everyone sin^2(arcsin u) = u^2 , thats what i thought it was

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2Oh man, I thought I was loosing it :/

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i got dw:1327181038255:dw

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but i'm not sure about my answer

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2wolfram disagrees http://www.wolframalpha.com/input/?i=integral+from+0+to+0.5+%28arcsin%28x%29%2Fsqrt%281x%29 but I don't trust wolfram anymore, lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't know man that question is hard to me :(

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0is it written correctly on the file you posted?

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2yeah, if there was an x^2 in the denom our lives would be about a million times easier

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let me check it again, I may write it wrong

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah you were right TuringTest I'm really sorry guys

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i'm sorry guys there is X^2

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2\[\frac{d}{dx}\sin^{1}x=\frac{1}{\sqrt{1x^2}}\]so \[u=\sin^{1}x\to du=\frac{1}{\sqrt{1x^2}}dx\]giving\[\int udu\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah that what i did so far , but i wanna know if i'm doing right TuringTest. Can you do until the end of it ?

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2\[\frac{d}{dx}\sin^{1}x=\frac{1}{\sqrt{1x^2}}\]I'm going to be lazy and not use the proper bound notation, just plug numbers in at the end. \[u=\sin^{1}x\to du=\frac{1}{\sqrt{1x^2}}\]giving\[\int udu=\frac{u^2}{2}=\frac{1}{2}(\sin^{1}x)^2_{0}^{1/2}=\frac{1}{2}[(\sin^{1}(1/2))^2(\sin^{1}(0))^2]\]\[=\frac{1}{2}[(\frac{\pi}{6})^20]=\frac{\pi^2}{72}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank You so much Turing that was very helpful
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