• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Help with Trig Substitution Integral Problem

  • Thread starter student93
  • Start date
85
0
1. Homework Statement

Question is attached in this post.


2. Homework Equations

Question is attached in this post.

3. The Attempt at a Solution

I've solved the problem via using x=asinθ where a=1

I've been able to integrate the problem to the point where I get cos^2(θ)/sin^2(θ), but can't seem to find a way to simply the problem further so that I can finish off the integration.

The answer to the question is √3 - π/3
 

Attachments

Last edited:

Curious3141

Homework Helper
2,830
86
1. Homework Statement

Question is attached in this post.


2. Homework Equations

Question is attached in this post.

3. The Attempt at a Solution

I've solved the problem via using x=atanθ where a=1

I've been able to integrate the problem to the point where I get cos^2(θ)/sin^2(θ), but can't seem to find a way to simply the problem further so that I can finish off the integration.

The answer to the question is √3 - π/3
Please show your steps in detail.
 
1,540
134
I've solved the problem via using x=atanθ where a=1

I've been able to integrate the problem to the point where I get cos^2(θ)/sin^2(θ), but can't seem to find a way to simply the problem further so that I can finish off the integration.

The answer to the question is √3 - π/3
I do not see how x=atanθ would help you in this problem .Instead try x=sinθ or cosθ.
 
85
0
85
0
Please show your steps in detail.
∫√(1-sin^2(θ))/(sin^2(θ) dθ = ∫cos^2(θ)/sin^2(θ) dθ

(I don't know how to simply the problem further, I know cos^2/sin^2=cot^2, but trying to get the integral of cot^2 isn't practical etc.)
 
85
0
Okay...Now rewrite cot2θ in terms of cosec2θ and proceed .
Thanks lol, I completely forgot about that identity since I haven't used that specific one in a long time etc.
 

Want to reply to this thread?

"Help with Trig Substitution Integral Problem" You must log in or register to reply here.

Related Threads for: Help with Trig Substitution Integral Problem

Replies
8
Views
2K
Replies
3
Views
772
Replies
1
Views
1K
  • Posted
Replies
16
Views
2K
  • Posted
Replies
3
Views
899
Replies
4
Views
2K
Replies
11
Views
1K
  • Posted
Replies
7
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top