Post #14 & #15

Sorry I didn't do the last blog. I guess the excitement of the holidays made me forgot.

Anyways post #14, I missed class two days this week so I have many questions.(*S is for the integral)

We learned about substitution, and I looked over my notes and examples to see if I could understand it. The only thing I see is that du is the derivative of u. Could someone explain the steps to a substitution problem?

Like what is the u of these problems? Then what do you do after the u and du step?
S(x^2+1)(2x)dx
Sx(x^2+1)^2dx
Also with e integration and ln integration, you have to use substitution in some problems?

I do know indefinite integration though. Sx^ndx=(x^n+1/n+1)+C (EQUATION) Examples:
1. Sx^3dx= (1/4)x^4+C 2. Sx^2+4x+9dx
(1/3)x^3+(4x^2/2)+9x+C
=(1/3)x^3=2x^2+9x+C


Now for post #15...we have been off a whole week!

I think I'm going to discuss definite integrals this time.
The formula for definite integration: bSa f(x)dx= F(b)-F(a) =NUMBER. First you integrate and put the little line with the b and a, and then you would just plug in to your formula. Example:

1. 3S0 x^2dx= (1/3)x^3 (and then you would put the little line with 3 and 0, but it is hard to type this on here)
(1/3)(3)^3-(1/3)(0^3)= 9

Now something that does confuse me is something like 4S0 absolute value of(x^2-9)dx I checked out calcchat.com but I don't understand what they did. Anyone can help with that?