Double integral solution

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1. Mar 12, 2016

Ekramul Towsif

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. Mar 12, 2016

blue_leaf77

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. Mar 12, 2016

geoffrey159

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.