Trigonometric substitution, What am i doing wrong?

[AMan24]

Homework Statement

Homework Equations

The Attempt at a Solution

Here is my answer, i get 1/24

For my first step i divided both terms under the radical by 4, then split 1/4 into (1/2)², i saw something very similar in my book so i did the same thing, but i just realized this has to be wrong. Whatever was in my book looked like this, but i guess there must be more to it

I finally figured it out, was supposed to factor out the 4, not divide by it

Here is the books answer, it's 1/12

I realize I am doing it differently than the books, but i just don't understand why my way is wrong. I've done it 3 times, very slowly and carefully. So there must be something I am not aware of. Please help me!

 

[jambaugh]

In your very first step you factored out the 4 in the radical, which becomes 2 outside the radical which... disappears.
You lost that factor of 2. Your second integral is 1/2 the original so your answer is 1/2 the correct answer.