# Thread: Integral problem involving arc sine

1. ## Integral problem involving arc sine

Hello all,

(integral sign) dt/ root(4-t^2)

thank you. Also, i know you use arc sin but as for the process?

2. Originally Posted by andrewsx
Hello all,

(integral sign) dt/ root(4-t^2)

thank you. Also, i know you use arc sin but as for the process?
$\frac{1}{\sqrt{4 - t^2}} = \frac{1}{2} \, \frac{1}{\sqrt{1 - (t/2)^2}}$. So to integrate, make the substitution u = t/2 and apply the usual formula ......

3. does anybody have a better answer...i don't get the previous post

4. May be you're not so familiar by remembering formulae. Another way could be using $x=\frac1u.$

5. Originally Posted by andrewsx
does anybody have a better answer...i don't get the previous post
What don't you get? The substitution? The integral becomes:

$\frac{1}{2} \int \frac{1}{\sqrt{1 - (t/2)^2}} \, dt = \int \frac{1}{\sqrt{1 - u^2}} \, du$ since dt = 2 du.

And you must have seen the standard form $\int \frac{1}{\sqrt{1 - x^2}} \, dx = Sin^{-1} x + C$ ......

6. Originally Posted by Krizalid
May be you're not so familiar by remembering formulae. [snip]
Indeed. That's why integral tables were invented.

7. ## Integral

Originally Posted by andrewsx
does anybody have a better answer...i don't get the previous post
Help.

How ever, if you don't understand what anybody did you can tray your own substitution in transform unknown integral to elementary. You can try with
t=2 Sin(x), t=2 Cos(x) or more elementary t=2x. Note: your integral is elementary and look for the properties of Sin(x),Cos(x),Tan(x) or Tg(x),Sinh(x),Cosh(x),Tanh(x) -> they are very usefull for substitution; and look up for trick for integration "per partes".
When you want to integrate it is THE MOST IMPORTANT to know elementary integrals and with them you will know integrate more complicate intagrals - most or all complicated integrals with substitution can be transformed in elementary.

Good luck.