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

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#### Solution

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`

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function

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