- #1

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## Homework Statement

Integrate (1 + x

^{2})

^{1/2}from -∏ to ∏

## Homework Equations

## The Attempt at a Solution

I substiuted x = tan(theta) but when I went to change the limits of integration I got 0 and 0. What am I doing wrong?

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- Thread starter cp255
- Start date

- #1

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Integrate (1 + x

I substiuted x = tan(theta) but when I went to change the limits of integration I got 0 and 0. What am I doing wrong?

- #2

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Better try [itex]x=\sinh u[/itex].

- #3

verty

Homework Helper

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This is not the mistake though, the mistake is doing the change of limits in the wrong direction.

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- #5

Ray Vickson

Science Advisor

Homework Helper

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## Homework Statement

Integrate (1 + x^{2})^{1/2}from -∏ to ∏

## Homework Equations

## The Attempt at a Solution

I substiuted x = tan(theta) but when I went to change the limits of integration I got 0 and 0. What am I doing wrong?

Use the fact that the integrand is even, to get

[tex]\int_{-\pi}^{\pi} \sqrt{1+x^2} \, dx = 2 \int_0^{\pi} \sqrt{1+x^2} \, dx.[/tex]

This type of issue comes up a lot when changing variables in defiinite integrals, so you need to be very aware of it.

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