1. ## Integral Problems

uo

2. I am not going to do the definite integral, rather I will find the anti-derivative and leave you to evaluate them at the endpoints.

3. Next one

4. Originally Posted by ThePerfectHacker
I am not going to do the definite integral, rather I will find the anti-derivative and leave you to evaluate them at the endpoints.
Can explain, perfecthacker, in your math ways, why if u = x, then du = 1 ?
Never have I encountered that before in my math ways?

Do you have your own math ways?

5. Originally Posted by ThePerfectHacker
I am not going to do the definite integral, rather I will find the anti-derivative and leave you to evaluate them at the endpoints.
Again, if u' = 1
Then u = x --------------???

Also, if v = arcsin(x)
Then v' = 1 / sqrt(1 -x^2) ------------???

then INT. [u]dv
= INT. [x / sqrt(1-x^2)]dx ---------where did you get dx?

6. Originally Posted by ticbol
Can explain, perfecthacker, in your math ways, why if u = x, then du = 1 ?
Never have I encountered that before in my math ways?

Do you have your own math ways?
In my other post in geometry, I talk about "rigorous" and how important it is to mathemations.

Now, the concepts of differenencials, splitting the dy and the dx as if they are fractions.

Like for example,
dy/dx=y
Then,
(1/y)dy=dx
Is not really acceptable among mathemations because they are not fractions. Thus, I use a more formal approach which does not involve splitting the denominator of the differencial.

I wrote a Calculus thread over here.
http://www.mathhelpforum.com/math-he...utorial-2.html

(The math program that is used to generate math code is math working properly now, thus you might not see everything).

In that thread I explain how I do integration via the substitution rule my way.

~~
And yes, that is my own techinque.