Question

Evaluate `int_0^1 int_(x^2)^x xy(x+y)dydx.`

Answer 1

We have, 

`I=int_0^1 int_(x^2)^x (x+y) dydx`

`I=int_0^1 [(x^2y^2)/2+(xy^3)/3]_(x^2)^x dx` 

`I=int_0^1 [x^4/2+x^4/3-x^6/2-x^7/3]dx` 

`I=[5/6.x^5/5-x^7/14-x^8/24]_0^1`

`I=1/6-1/14-1/24` 

`I=3/56`