Whats the average value of the function $ f(x,y) = 4^6xy^3 $ over the region $$(x,y) : 0 \leq x < \infty, 0 \leq y \leq \frac{1}{4^2 +x^2}$$ ?
I tried finding the volume by solving $$ \int_0^\infty\int_0^\frac{1}{4^2+x^2} 4^6xy^3 dydx $$ and then dividing by the area to get the average height. However when i attempted to compute the double integral I obtained a divergent integral (x approaching infinity).