- #1

- 15

- 0

## Homework Statement

\int_0^{\infty} sin(ax) / sqrt(x) dx

## Homework Equations

## The Attempt at a Solution

I thought of using integration by parts, but that gets me nowhere. I'm not sure how to go about this problem.

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In summary, the conversation discusses the integration of sin(ax)/sqrt(x) using different techniques. One approach involves integration by parts, but it does not provide a solution. Another approach uses a substitution and extends the integral to the entire real axis to obtain the imaginary part of ei au^2. This method ultimately leads to the result that the integral of exp(-a y^2) over the real line is sqrt(pi/a) as long as Re(a) > 0. The conversation concludes with an inquiry for a simpler approach.

- #1

- 15

- 0

\int_0^{\infty} sin(ax) / sqrt(x) dx

I thought of using integration by parts, but that gets me nowhere. I'm not sure how to go about this problem.

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- #2

Science Advisor

Homework Helper

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If you first do a substitution to u = x

Anyone for an easier approach?

- #3

- 15

- 0

Thanks. That's exactly what I needed.

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