A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
in Substitution Rule
anonymous
 4 years ago
in Substitution Rule

This Question is Closed

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

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

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

anonymous
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0Why can't we do both?

myininaya
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0ok Thank you a lot guys :)

TuringTest
 4 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 ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes arcsin(sin u) = u by definition of the inverse function

TuringTest
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0could we have just used the substitution:\[u = \sin^{1}(x)\]

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

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

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

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0wait 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
 4 years ago
Best ResponseYou've already chosen the best response.2Oh man, I thought I was loosing it :/

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

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

TuringTest
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0I don't know man that question is hard to me :(

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

TuringTest
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0let me check it again, I may write it wrong

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

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

TuringTest
 4 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
 4 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
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0Thank You so much Turing that was very helpful
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.