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Calculus/Definite Integrals

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Expert: Alon Mandes - 10/2/2009


Question
Hi Alon,
I am trying to answer my assignment in Calculus.  It has been hours but I am still confused.
I am trying to evaluate the definite integral:
Integral limit 1 to 8 {x^(1/3)-x^(-1/3)}dx

Appreciate so much your help.
Thanks.


Answer
Hello Libby,
Sorry, my mistake, here's the correct answer :
From table of integrals we can notice that ∫x^(m/n) dx = 1/[(m/n)+1]x^(m/n +1) . Therefore :
∫x^(1/3) dx = (3/4)x(4/3) & ∫x^(-1/3) dx = (3/2)x^(2/3) . Hence ,
8
∫ x^(1/3)-x^(-1/3) dx =
1
(3/4)x^(4/3) {1->8} - (3/2)x^(2/3) {1 ->8} =
[(3/4)*8^(4/3)]-(3/4)+[(3/2)*8^(2/3)]-(3/2)=
15.75

Alon.

Calculus

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Alon Mandes

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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 .

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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".

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

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M.A in Mathematics & Bs.c in Electronics.

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