I have two multivariable functions, and I want to calculate where they intersect on the outer bounds of $x$ and $y$ between the graphs of $f(x,y)$ and $g(x,y)$.
The functions are:
$f(x,y)=x^2+4y^6$
$g(x,y)=\sin{(x)}+\frac{1}{5}y+4$
I need to find these intersections in order to calculate the volume under the graph of $f(x,y)$ with a double integral that is limited by $g(x,y)$ on the $z$-axis. I am a beginner regarding multivariable calculus, so can anyone help me with this?
Here is an image of the problem:
