Integrating the Square Root of a Polynomial: (4 - x^2)^1/2

[optics.tech]

Hi everyone,

How to integrate the (4 - x^2)^1/2?

Thank in advance

 

[Linear Space]

Use a trigonometric substitution:

$$\begin{gathered}<br /> \int {\sqrt {4 - x^2 } dx \Rightarrow } \left[ {\begin{array}{*{20}c}<br /> {x = 2\sin \theta } \\<br /> {dx = 2\cos \theta d\theta } \\<br /> <br /> \end{array} } \right] \hfill \\<br /> \int {2\cos \theta \sqrt {4(1 - \cos ^2 \theta )} } d\theta = 2\int 2 \sin \theta \cos \theta d\theta \cdot \cdot \cdot \hfill \\ <br /> \end{gathered}$$

I think you can get it from there.

 

[Defennder]

Wow, that's some Latex mastery you have there.