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Definite integral with complex result?

  1. Dec 10, 2012 #1
    1. The problem statement, all variables and given/known data
    ∫ 3+ x√x from -1 to 4


    2. Relevant equations



    3. The attempt at a solution
    ∫ 3+ x√x from -1 to 4 = 3x+(2(x^5/2))/5 evaluated from -1 to 4

    (12 + (2(4^5/2))/5) +(3 +(2(-1)^5/2)/5) ?

    15+64/5 +(2(-1^(5/2))/5)

    139/5 -(2(-1^(5/2)))/5

    139/5 -2i/5

    is that right?
     
  2. jcsd
  3. Dec 10, 2012 #2
    Yes:

    http://www.wolframalpha.com/input/?i=integrate+3+++x*sqrt(x)+from+-1+to+4
     
  4. Dec 10, 2012 #3

    Mark44

    Staff: Mentor

    Because of the term with the square root, the integrand is defined only for x ≥ 0. What is the complete statement of the problem?

    Although there is a version of the square root function whose domain includes negative numbers, this is usually not presented in calculus courses.
     
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