Integrating the Integrand: Solving a Double Integral

[Ekramul Towsif]

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 :(

 

[blue_leaf77]

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.

 

[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.