I am having problems doing problems when I am given a u as in a form u^2 = this and that.
If I were to pick my own value, I'd usually just pick "u", even if it's rooted. But whenever I have to take it squared, or u rooted, I encounter problems.
Usually I just integrate, and then substitute for dx.
With u^2's I get really confused.
For example, in c4, exercise 6H number 4.
I am given x√(2-x) dx
There needs to be an EXACT value to be found, and all that has to be integrated with limits from 2 to 0.
While I did took u as a 2-x, I could only find the approximate value, while when looking at the worked answer, it was suggested I take u^2. I would have never though of that.. and I am struggling in knowing when to take u^2 or rooted u or normal u.
Because by taking u^2, you'd end up with a surd fraction, and it will also make you change limits with one of them being root 2.
So yeah.. I am really having troubles with these... any advice from someone who is good or has experienced the same thing?