Integrating ∫√(2+2sinθ) using (2+2sinΘ)(2-sinΘ)

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Homework Help Overview

The discussion revolves around integrating the expression ∫√(2+2sinθ). Participants are exploring the integration techniques and transformations related to this trigonometric integral.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the identity (2+2sinΘ)(2-sinΘ)=4-4sinΘ^2 as part of their integration strategy. There are attempts to manipulate the integrand by multiplying and dividing by √(2-2sinΘ). Questions arise regarding the resulting expression and whether any substitutions have been considered.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the steps taken. There is a focus on clarifying the transformations applied to the integral, and some guidance is offered regarding potential missing elements in the expression.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the methods they can explore. There is an emphasis on ensuring all components of the integrand are accounted for in their manipulations.

aerograce
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Homework Statement



How to integrate∫√(2+2sinθ)

Homework Equations



Making use of (2+2sinΘ)(2-sinΘ)=4-4sinΘ^2

The Attempt at a Solution



Multiply and dividing the integrand by √2-2sinΘ
 
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aerograce said:

Homework Statement



How to integrate∫√(2+2sinθ)

Homework Equations



Making use of (2+2sinΘ)(2-sinΘ)=4-4sinΘ^2

The Attempt at a Solution



Multiply and dividing the integrand by √2-2sinΘ

Show us what happened when you did that...
 
LCKurtz said:
Show us what happened when you did that...

It becomes,

∫ 4cosΘ^2/√(2-2sinΘ)
 
aerograce said:
It becomes,

∫ 4cosΘ^2/√(2-2sinΘ)

Isn't there a square root missing in the numerator? Have you tried any substitutions?
 
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