Attached is a problem I hand wrote. I don't get why on the first step, it has to be multiplied by -(1/2). is that part of a rule? Thanks!

Printable View

- May 8th 2010, 08:24 PMfabxxDefinite Integral Problem
Attached is a problem I hand wrote. I don't get why on the first step, it has to be multiplied by -(1/2). is that part of a rule? Thanks!

- May 8th 2010, 08:46 PMRandom Variable
simple substitution

let

then

which means that

so - May 8th 2010, 08:48 PMfabxx
I flipped through my textbook and it didn't say that it had to multiply (-1/2). How come it needs to multiply that? I'm still confused :(

- May 8th 2010, 08:53 PMAllanCuz
You do know what the chain rule is? What we're looking for when we take

is some function that when we differentiate it, it becomes . In other words,

So to see why you need the -1/2 differentiate the answer and see what you get. You will notice that without the -1/2 you DO NOT obtain what was inside the integral! - May 8th 2010, 08:58 PMRandom Variable
Because when you make the substitution, you switch from integrating with respect to to integrating with respect to . To do that you need to know how to write in terms of . Have you covered integration by substitution in class?

- May 8th 2010, 09:02 PMfabxx
I understand that if I don't get (-1/2) it won't be the original problem and i do understand the chain rule.

if its the chain rule

should the anti differentiation of (-2t) = -2 [(t^2)/2] ?

Thanks! - May 8th 2010, 09:05 PMAllanCuz
- May 8th 2010, 10:03 PMchiph588@

So