Evaluate; ∫∫xy(x+y)dxdy over the area between y = x2 and y = x.

Evaluate;     

The area is bounded by the curves 

y = f1(x) = x2, y = f2(x) = x. , 

like--- 

When f1(x) = f2(x), x2 = x, i.e., x = 0, x = 1, i.e., the area of integration is bounded by 

y = x2, y = x, x = 0 , x = 1 

In fig. x varies from x = 0 to x = 1 and y varies from y = x2 to y = x

∴ 

= 

= 

= 3/56