AboutAlon Mandes Expertise Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse, infinite series & convergence,Divergence & Rotor.
Kind of question I can't answer : Economics,Combinatorics,Statistics, & Fractions.
Experience 1. I'm a team member of mathnerds (math site for answering questions)
2. I'm a team member in the Student's Union of the Technion, helping
students who have problems in mathematics.
3. 2 years of experience as a math teacher in college.
4. I give free homework help for high school students in
Mathematics & Physics.
Expert: Alon Mandes Date: 7/17/2008 Subject: need help
Question can uyou please tell me what is the integration of square of <dx>
Answer I'm not quite sure that I understood what you meant, but here's
my answer : dx is the infinitesimal (or flux , according to Newton)
value of change to be summed in the integral. It can never be squared or operated by an operator, because the operator is d. For
example : d(f(x))=f'(x)dx. Or d(2x^2-5x)=(4x-5)dx. The only form that
you may see (dx)^2 is in multivariable function. For example :
z=f(x,y) --> dz=sqrt((dx)^2+(dy)^2) it's called the differential of z.
The other Form of squaring the derivative is by calculating arc length : ds=sqrt[1+(dy)^2/(dx)^2] --> L=Integral[ds]. We make coordinates transformation : x=x(t),y=y(t) & we gain
L=Integral[qsrt(x'(t)^2+y'(t)^2]dt. Note that we converted (dx)^2
& (dy)^2 with dt.
