A community for students.
Here's the question you clicked on:
 0 viewing
2bornot2b
 4 years ago
Evaluate the integral \[\int\frac{1}{(x^2\sqrt{x^216)}}dx\] using the substitution \[x=4\sec\theta\]
This question is originally posted by SteelSeries
2bornot2b
 4 years ago
Evaluate the integral \[\int\frac{1}{(x^2\sqrt{x^216)}}dx\] using the substitution \[x=4\sec\theta\] This question is originally posted by SteelSeries

This Question is Closed

SteelSeries
 4 years ago
Best ResponseYou've already chosen the best response.0I wonder if many people know Calc II here...

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.2\(x=4\sec\theta \implies dx=4\tan\theta \sec\theta d\theta \), substituting that we get: \[\int \frac{4\tan\theta \sec\theta}{16\sec^2\theta\sqrt{16\sec^2\theta16}}d\theta=\int \frac{4\tan\theta}{16\sec\theta\cdot 4\tan\theta}=\frac{1}{16}\int \cos\theta=\cdots \]

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.2Don't forget to substitute back for \(x\).

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.4\[dx=4sec( \theta) tan( \theta) d \theta \] \[\int\limits_{}^{}\frac{ 4 \sec(\theta) \tan(\theta) d \theta}{4^2 \sec^2(\theta) \sqrt{4 ^2 \sec^2(\theta)16}} \] \[\frac{4}{4^2}\int\limits_{}^{}\frac{\tan(\theta) d \theta}{\sqrt{16} \sec(\theta) \sqrt{\sec^2(\theta)1}}\] \[ \frac{1}{4} \cdot \frac{1}{\sqrt{16}} \int\limits_{}^{} \frac{\tan(\theta) d \theta}{\sec(\theta) \sqrt{\tan^2(\theta)}} \] \[\text{ Assume } \tan(\theta)>0 =>\tan(\theta)=\tan(\theta)\] So we have \[\frac{1}{16}\int\limits_{}^{}\cos(\theta) d \theta= \frac{1}{16}\sin(\theta)+C\] Recall the sub: \[x=4 \sec(\theta) => \sec(\theta)=\frac{x}{4} (=\frac{hyp}{adj})\] So opposite=... \[opp=\sqrt{x^24^2}=\sqrt{x^216}\] So we have the answer is \[\frac{1}{16} \frac{\sqrt{x^216}}{x}+C\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.4dw:1328289591112:dw

SteelSeries
 4 years ago
Best ResponseYou've already chosen the best response.0Wow, thanks guys, that really helps a lot!

2bornot2b
 4 years ago
Best ResponseYou've already chosen the best response.0So @steelseries, remember the tricks :) to increase your probability of getting answers. OK?

SteelSeries
 4 years ago
Best ResponseYou've already chosen the best response.0Yeah, will do, thanks Captain!

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.2What are those tricks? We want to know them too :P

2bornot2b
 4 years ago
Best ResponseYou've already chosen the best response.0If so then here is the real story. http://openstudy.com/users/steelseries#/updates/4f2c1192e4b0e1bedb5d1d04
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.