How can I fix up the singularity?

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Homework Help Overview

The discussion revolves around evaluating two integrals, one involving a singularity at the lower limit and the other involving a trigonometric function in the denominator. The subject area includes calculus and integration techniques.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore various methods for addressing the singularity in the first integral, including the possibility of using power series. There is also mention of integration by parts for the second integral, with a suggestion to rearrange the function involved.

Discussion Status

Some participants have offered hints and suggestions, indicating a collaborative effort to explore different approaches. The discussion appears to be productive, with multiple lines of reasoning being considered.

Contextual Notes

There is a noted singularity in the first integral, and participants are questioning how to handle it effectively. The original poster acknowledges the involvement of the Error function but is uncertain about the path to reach it.

ftarak
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Homework Statement

I = \int^{2}_{0} (1-e^{-x})/\sqrt{x}

I=\int^{2}_{0.1}x/sin^2(x)

Homework Equations


The Attempt at a Solution


I tried to integrate by part, but I approached to trivial solution. I know that the answer is involved with Error function, but I don't know how I could reach the answer. so does anybody have any idea? please help.
 
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I am not sure but I am thinking about power series solution for the first integral. How can I fix up the singularity?
 


u^2 = x
 


For the second one, integration by parts is your friend. Just remember to rearrange sin^2(x) first.
 


thank you guys, your hints were so helpful.
 

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