Help with Trig Substitution Integral Problem

student93

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

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Curious3141

Homework Helper
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

Tanya Sharma

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.

student93

I do not see how x=atanθ would help you in this problem .Instead try x=sinθ or cosθ.
That was a typo, I actually did use asinθ.

student93

∫√(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.)

Tanya Sharma

That was a typo, I actually did use asinθ.
Okay...Now rewrite cot2θ in terms of cosec2θ .

student93

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.

"Help with Trig Substitution Integral Problem"

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