Question

Evaluate `int_0^1 int_0^(x2) y/(ex) dy  dx` 

Answer 1

let I = `int_0^1 int_0^2 e^ (y/x) dy   dx` 

=` int_0^1[e^(y/x)/(1/x)]^(x^2)0  dx` 

=`int_0^1 (e^x-1)/(1/x).dx`

= `int_0^1 x.e^x  dx-int_0^1 x.dx` 

=`[x.e^x-e^x]^(1/0)-[x^2/2]^(1/0)`

= `e-e+1 -1/2` 

∴ `I = 1/2`