Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

i have a derivation of a physical equation, where there is an equation

$$\int mv \gamma \,\textrm{d}v = \frac{m}{2}\int \gamma \, \textrm{d}(v^2)$$

Q1: How did we derive right side from left one? Could anyone explain this step by step or provide me with names of the integration rules applied here so i can google it myself.

share|improve this question
add comment

2 Answers 2

up vote 2 down vote accepted

$$ \frac{dv^2}{dv}=2v \Rightarrow \frac{dv^2}2=vdv $$

share|improve this answer
    
Thanks... a simple derivation explains everything. –  71GA Nov 26 '12 at 16:29
1  
In fact sometimes it is easier to me to learn integration through diferentiation. –  71GA Nov 26 '12 at 16:29
add comment

This follows directly from

$$\int A f(x)\, \text dx= A\int f(x)\, \text dx$$

and a substitution.

share|improve this answer
    
For what it's worth, I'll mention that $\mbox{d}(v^2)$ is shorthand for $\dfrac{\mbox{d}v^2}{\mbox{d}v}\mbox{d}v$. –  Clive Newstead Nov 26 '12 at 15:58
    
What yo just said is that i can put a constant in front of an integral? TY –  71GA Nov 26 '12 at 16:28
    
@71GA $m$ is just a constant. Thus you can move it out of the integral. –  Argon Nov 26 '12 at 16:29
    
Hello there Argon! pretty near 6k! –  amWhy Nov 27 '12 at 2:05
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.