Double integral solution

  • #1
Ekramul Towsif
6
0

Homework Statement


##\int_{z=0}^5 \int_{x=0}^4 \Big( \frac{xz}{ \sqrt{16-x^2}} +x \Big)dxdz##

Homework Equations


double integration

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 :(
 

Answers and Replies

  • #2
blue_leaf77
Science Advisor
Homework Helper
2,637
786
how do i integrate the term ##\frac{xz}{ \sqrt{16-x^2}}##
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.
 
  • #3
geoffrey159
535
72
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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