find the values for K which the given integral converges:

Question

0<y<x^k , 1<x<∞

∫∫ y^b dA

0<x<1 , 0<y<x^k

∫∫ x^a dA

Answer 1

I will assume that dA means dx dy

For both integrals, the integration of y should be carried out first. 

For the first integral this results in integral x^k dx with limits  1 to infinity. This converges for k <0

For the second integral this results in integral x^k dx with limits zero to 1. 

 This converges for k > -1