1. ## understanding trig. substitution

http://www.mathhelpforum.com/math-he...-4-x-2-dx.html

hi,

can anyone explain why sub X = 2 sin (theta) ?

2. Originally Posted by Chris0724
why sub x = 2 sin (theta) ?
Inorder to do it by integration by substitution

-What's the main question you have?

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--If it is that we can substitute this directly in the formula
----than the formula is also derived like this

3. hi,

i understand that in order for the substitution to work, we have to sub in x = 2 sin (theta)

but is there any other term that will work other than 2 sin (theta) ?

How do we know, by looking at the qns, we have to sub in 2 sin theta ?

thanks!

4. It's just a matter of manipulating it to use certain trigonometric identities.

If your integrand contains something of the form:
• $\sqrt{a^2 - x^2}$ use $x = a\sin \theta$ so you can use the identity: $1 - \sin^2 \theta = \cos \theta$
• $\sqrt{x^2 - a^2}$ use $x = a\sec \theta$ so you can use the identity: $\sec^2 \theta - 1 = \tan \theta$
• $\sqrt{a^2 + x^2}$ use $x = a\tan \theta$ so you can use the identity: $1 + \tan^2 \theta = \sec^2 \theta$

The question posed in this thread is an example of the first.

5. Or if you've dealt with hyperbolic trigonometry, you can use this identity : $\cosh^2(x)-\sinh^2(x)=1$

So if you have $\sqrt{a^2+x^2}$, you can substitute $x=a \sinh(t)$ and hence $\sqrt{a^2+x^2}=a \cosh(t)$