Integrating Sinx/x^2 from Y=4 to Y=0 with x=2 and x=√y

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Homework Help Overview

The discussion revolves around the integration of the function sin(x)/x² over a specified region defined by the limits Y=4 to Y=0 and x=2 to x=√y. Participants are exploring the setup and evaluation of this double integral.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the possibility of using an integral table for the integral of sin(x)/x² and suggest expanding sin(x) as an infinite series for further analysis. There is also a mention of changing the order of integration and verifying the correctness of the approach taken.

Discussion Status

Some participants have provided guidance on potential methods for solving the integral, while others express uncertainty about the correctness of their approaches. The discussion reflects a mix of interpretations and attempts to clarify the problem setup.

Contextual Notes

There is a mention of a reference sheet that contains a final answer, but participants are questioning the validity of their methods and the assumptions made during the integration process.

theaviator
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Y=4 x=2
∫ ∫ Sinx ∕ x^2 dx dy
Y=0 x=√y
 
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Can one find an integral table with

[tex]\int \frac{sin\,x}{x^2}\,dx[/tex] ?

Alternatively, expand sin x as an infinite series, divide by x2 and solve for each term.
 
i changed the order of the integration...the final answer i had is the same one in the sheet from which i get the problem...but i don't know id the way i solved it is right or wrong...please HELP...
X=2 y=x^2
∫ ∫ sinx/x^2 dx dy
X=0 y=0

X=2 y=x^2
= ∫ [(sinx/x^2)y] dx
X=0 y=0

X=2
=∫ sinx dx
X=0
X=2
= [ -cosx]
X=0

= -cos2+cos(0)= 1-cos2
 
That is correct.
 

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