Double Integral 232.q1.5a Calculation

[karush]

$\tiny{232.q1.5,a}$
\begin{align*}\displaystyle
I_a&=\iint\limits_{R} xy\sqrt{x^2+y^2} \, dA \\
R&=[0,2]\times[-1,1]
\end{align*}

would this be

$$\int_{-1}^{1} \int_{0}^{2}xy\sqrt{x^2+y^2} \,dx \, \, dy $$

 

[jvicens]

Yes, that is correct. The given integral represents the double integral of the function $xy\sqrt{x^2+y^2}$ over the region $R=[0,2]\times[-1,1]$. This notation is often used in mathematics to represent a double integral, with the inner integral representing the integration with respect to the first variable and the outer integral representing the integration with respect to the second variable. It is important to specify the limits of integration for each variable to accurately evaluate the integral.