- #1

John O' Meara

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## Homework Statement

Find by letting [tex]U^2=(4 + x^2) [/tex]the following [tex] \int_0^2\frac{x}{\sqrt{4 + x^2}}dx[/tex]?

I can solve it by letting [tex]\mbox{x=2} tan(\theta)[/tex], But I want to be able to do it by substitution.

## The Attempt at a Solution

[tex] \frac{du}{dx}=\frac{d\sqrt{(4+x^2)}}{dx}=\frac{x}{\sqrt{4+x^2}}\mbox{, therefore du}=\frac{x}{u^\frac{1}{2}}\times dx\\[/tex] Therefore the integral is [tex] \int_{x=0}^{x=2}\frac{1}{u^\frac{1}{2}}du=[/tex]0.26757, it should be [tex] 2(\sqrt{2}-1)[/tex]. Can you tell me where I went wrong. Thanks for the help.

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