In regards to the following figurate of $f(x,y)=x$ in which $a=1$ and $b=10$, I was having some difficulty determining the boundaries of integration for the double integral. I assumed that $x=[1,10]$ and $y=[1,10]$. I also then tried $x=[1,10]$ and $y=[1,x]$ but the answer is coming up as incorrect when I compute the actual integral. I am also integrating with respect to $y$ first.
Am I making a mistake in the boundaries or computing the actual integral?
You can use cylindrical coordinates such as below:
$f(x,y) = rcos\theta$
Thus $$I = \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_{1}^{10} rcos\theta rdrd\theta$$
$$I = \frac{1998}{3}$$