Question Number 100074 by kungmikami last updated on 24/Jun/20

Answered by smridha last updated on 25/Jun/20

∫_0 ^1 [∫_0 ^(√y) (x^2 y+xy^2 )dx]dy  =∫_0 ^1 dy [(1/3)x^3 y+(1/2)x^2 y^2 ]_0 ^(√y)   =∫_0 ^1 [(1/3)y^(1+(3/2)) +(1/2)y^3 ]dy  =[(1/3).(y^(2+(3/2)) /(2+(3/2)))+(1/8)y^4 ]_0 ^1   =(2/(21))+(1/8)=((37)/(168))(unit)^2