Improper Integrals

Concept (Improper Integral). If f(x,y)0f (x, y)\ge 0 on D, then the improper integral Df(x,y)dA\displaystyle\iint\limits_Df (x, y)dA can be computed by evaluating the iterated integral and determining convergence or divergence of the single variable improper integrals. A similar situation arises for triple integrals.



Practice: Improper integrals

Determine if the following integral converges. If it does, compute the integral.
001x1+y2dxdy\int_0^\infty \int^1_0 \frac{x}{1+ y^2} dx\, dy

Practice: Improper integrals

Determine if the following integral converges. If it does, compute the integral.
001xydxdy\int_0^\infty \int^1_0 \frac{x}{\sqrt y} dx\, dy