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Calculus/Trapezoidal Rule

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Expert: Alon Mandes - 5/10/2009


Question
evaluate the integral

e^x^2 with lower limit 1 and upper limit 2
using trapezoidal rule

Answer
Trapezoidal Rule :
b
∫f(x)dx ~  Δx[½f(xo)+f(x1)+f(x2)+...½f(xn)], where :
a

Δx=(b-a)/n
xn=a+kΔx , k=0,1,2,3,...,n

In our case :
We choose n=10, thus Δx=(2-1)/10 = 0.1 ,
xo=1 , x1=1.1 , x2=1.2 , x3=1.3 , x4=1.4 , x5=1.5 , x6=1.6 ,
x7=1.7 , x8=1.8, x9=1.9 , x10=2 .

2
∫f(x)dx ~  0.1[½f(1)+f(1.1)+f(1.2)+f(1.3)+f(1.4)+f(1.5)+f(1.6)+
1
              +f(1.7)+f(1.8)+f(1.9)+½f(2)]

~ 0.1[1.35+3.35+4.22+5.41+7.09+9.48+12.93+17.99+25.53+36.96+27.29]
~ 15.16

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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