Help with trigonometric substitution

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Homework Help Overview

The discussion revolves around evaluating the integral of the function (1)/(x^2√(36-x^2)), with a focus on trigonometric substitution techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of the substitution X=6sinθ and the resulting expressions for dx and √(36-x^2). There are questions about the integration of csc²θ and the simplification of terms involving cos(θ). Some participants express confidence in knowing the answer but are prompted to show their work for clarity.

Discussion Status

The discussion is ongoing, with participants providing feedback on each other's attempts. There is a recognition of the need to express the integral in terms of x without trigonometric functions, indicating a productive direction in the exploration of the problem.

Contextual Notes

Participants are encouraged to show their work to identify errors, and there is a mention of a constant that needs to be considered in the final expression. The original problem setup and the use of trigonometric identities are under examination.

ronybhai
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Homework Statement



integral (1)/(x^2sqrt(36-x^2)

Homework Equations





The Attempt at a Solution


I found X=6sinθ dx=6cos
√(36-x^2)=√(36-sin^2θ)=6cosθ
i think the problem is that i am not getting integral of ∫csc^2θ
 
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ronybhai said:

Homework Statement



integral (1)/(x^2sqrt(36-x^2)

Homework Equations





The Attempt at a Solution


I found X=6sinθ dx=6cos
√(36-x^2)=√(36-sin^2θ)=6cosθ
i think the problem is that i am not getting integral of ∫csc^2θ

You should. Show the rest of your work so someone can tell you where you went wrong.
 
Dick said:
You should. Show the rest of your work so someone can tell you where you went wrong.

i know the answer which is -√(36-x^2)/36x+C
 
ronybhai said:
i know the answer which is -√(36-x^2)/36x+C

That's not the rest of your work, that's what I asked for. You've got a cos(θ) and the numerator and cos(θ) in the denominator. They cancel. What's left?
 
ronybhai said:
i know the answer which is -√(36-x^2)/36x+C

The integral is -cotθ + C
 
KDeep said:
The integral is -cotθ + C

That's part of it. There's also a constant around. But like we were talking about in your last post there is a way to express -cot(arcsin(x/6)) as a function of x without any trig functions. That's what the books answer is.
 

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