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Calculus/Calculus (basic trig integrals)

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Expert: Alon Mandes - 5/23/2009


Question
WHY is integral of sin equal to -cos?  AREA under Sin curve from 0 to Pi is POSITIVE, but values of -cos from 0 to Pi/2 are NEGATIVE.  Can't be right.  (Even though all math books and websites say it is.) What did I miss?

Answer
1st of all d/dx sin[x] = Cos[x] & not -Cos[x] !!
Lets prove the derivative by definition :
Lim  [f(x+h)-f(x)]/h = f'(x)
h->0
Lim  [sin(x+h)-sin(x)]/h =
h->0
Lim  [sin(x)cos(h)+sin(h)cos(x)-sin(x)]/h =
h->0
Lim   [sin(x)cos(h)-sin(x)]/h + [sin(h)cos(x)]/h =
h->0
Lim  sin(x)[cos(h)-1]/h + Lim  cos(x)*[sin(h)/h] = cos(x)
h->0                      h->0
Becuase
Lim  Sin[h]/h = 1  
h->0
&
Lim  (Cos[h]-1)/h = 0
h->0

Alon.

Calculus

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Alon 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,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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