A community for students.
Here's the question you clicked on:
 0 viewing

This Question is Closed

tsghernan
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{1}^{9} \frac{ 1 }{ \sqrt{x*\sqrt{1+\sqrt{x}}} } \delta x \] (The integral is between 9 and 1

g152xx
 2 years ago
Best ResponseYou've already chosen the best response.0@TuringTest is here so have no fear ! :)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0Why do some people think I am a math demigod? I have no idea.... at least not yet.

cnknd
 2 years ago
Best ResponseYou've already chosen the best response.1try rewriting this with fractional powers instead of nested sqrts

cnknd
 2 years ago
Best ResponseYou've already chosen the best response.1then do a usubstitution where u = sqrt(x) (i'm just eyeballing this but it seems like this should work)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0you ought to try some of the things you suggest or it just becomes a flood of ideas rather than an clear approach that will help the asker.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4No, substitute u = 1 + x^(1/2) Then du = (1/2)x^(1/2) dx and then easy to solve from that point.

cnknd
 2 years ago
Best ResponseYou've already chosen the best response.1heh, same thing, just off by 1 (du is still the same)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0@tcarroll010 yes, I agree :)

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4@cnknd , it is necessary to isolate that term of "1" into u along with the x^(1/2)

cnknd
 2 years ago
Best ResponseYou've already chosen the best response.1i don't think it's all that difficult to integrate (1+u)^(1/4) rather than u^(1/4)

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4\[2\int\limits_{}^{}\frac{ du }{ \sqrt{u} }\]

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4\[= 4\sqrt{u}\]Now, just put the expression for u back in.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4\[4\sqrt{1 + \sqrt{x}}\]And you're done.

cnknd
 2 years ago
Best ResponseYou've already chosen the best response.1@tcarroll010 you forgot the a 2nd sqrt. it's \[2\int\limits_{2}^{4}\frac{ du }{ \sqrt{\sqrt{u}} }\]

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4Did not forget. Go back and look at the du equation. sqrt(x) is already in it.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4They get resolved in the du equation. Simply take the derivative of my answer and you'll see.

cnknd
 2 years ago
Best ResponseYou've already chosen the best response.1the first sqrt from the original expression covers both the x and the sqrt(1+sqrt(x)) unless my eyes are deceiving me.

g152xx
 2 years ago
Best ResponseYou've already chosen the best response.0@cnknd  @tcarroll010 is right, take a look again.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4Simply rewrite the original equation to\[\frac{ 1 }{ \sqrt{x}\sqrt{1 + \sqrt{x}} }\]and then it will be clearer. Again, just take the derivative of my answer and you'll get the original equation, written either way.

cnknd
 2 years ago
Best ResponseYou've already chosen the best response.1original integrand was: \[\frac{ 1 }{ \sqrt{x \sqrt{1+\sqrt{x}}} }\]

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4yes, which is the same as my rewrite.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0@cnknd  @tcarroll010 is right  he is making use of this:\[u = 1 + x^{1/2}\]Then\[du = (1/2)x^{1/2} dx=\frac{dx}{2\sqrt{x}}\]

cnknd
 2 years ago
Best ResponseYou've already chosen the best response.1let \[A = \sqrt{1+\sqrt{x}}\] the original integrand would be: \[\frac{ 1 }{ \sqrt{xA} }\] and your rewrite is: \[\frac{ 1 }{ \sqrt{x}*A }\] im pretty sure those are different

tsghernan
 2 years ago
Best ResponseYou've already chosen the best response.0I can solve it. Thank you guys

cnknd
 2 years ago
Best ResponseYou've already chosen the best response.1if you want to double check your answer, here's wolframalpha's solution: http://www.wolframalpha.com/input/?i=integrate+%281%2Fsqrt%28x*sqrt%281%2Bsqrt%28x%29%29%29%29

tsghernan
 2 years ago
Best ResponseYou've already chosen the best response.0tcarroll010 was right. The best way is substitute u = 1 + x^(1/2)

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0oh  sorry @cnknd  I thought you were wondering where the \(\sqrt{x}\) went. you are right  there should be an extra sqrt there.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0@tsghernan  please take note of what @cnknd was saying as well  there is an extra sqrt to put in

cnknd
 2 years ago
Best ResponseYou've already chosen the best response.1thank you sir moderator :) and yea u = 1 + x^(1/2) is easier than what i suggested

tsghernan
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. I know it. I verified the result with the mathematica soft. I reached it. Thank you a lot

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4I do believe @cnknd has a point. It looks like \[2\int\limits_{}^{}\frac{ du }{ \sqrt[4]{u} }\]is the integral to be considered. How does that look to you now, @cnknd?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4and then (8/3)u^(3/4) with the eventual substitution of u in terms of x. Is that what you are getting?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4Good catch @cnknd !

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.4So, the answer is derived with a combination of my substitution equation of u = 1 + x^(1/2) (to resolve the other x^(1/2), that part is correct ) and @cnknd 's correction on the exponent on u going from 1/2 to 1/4.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0nice to see a "team" working towards a solution :)
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.