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Double integral solution

  1. Mar 12, 2016 #1
    1. The problem statement, all variables and given/known data
    ##\int_{z=0}^5 \int_{x=0}^4 \Big( \frac{xz}{ \sqrt{16-x^2}} +x \Big)dxdz##
    2. Relevant equations
    double integration

    3. The attempt at a solution
    how do i integrate the term ##\frac{xz}{ \sqrt{16-x^2}}## though i know that ##\int x \, dx = \frac{x^2}{2}##
    pls help me thoroughly :(
     
  2. jcsd
  3. Mar 12, 2016 #2

    blue_leaf77

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    Science Advisor
    Homework Helper

    The method used to solve that integral was most likely already covered in your past teacher's speeches.
    Use substitution method, in particular ##u=16-x^2##. From this compute ##du/dx## and the new integral limits.
     
  4. Mar 12, 2016 #3
    The integrand ##f(x,z)## is undefined when ##x=4##.
    You will have to discuss integrability of ## x \to f(x,z) ## on ##[0,4[##, and of ## z \to \int_0^4 f(x,z) \ dx ## on ## [0,5]##.
    If you can justify this, your double integral is well-defined and you can evaluate the integrals in any order you like.
     
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