How Can You Evaluate This Complex Double Integral?

[nameVoid]

$$\int_{1}^{2}\int_{y}^{y^3}e^{\frac{x}{y}}dxdy$$
$$\int_{1}^{2}ye^{y^2}-eydy$$
taking u = y^2
$$\frac{1}{2}\int_{1}^{4}e^udu-\int_{1}^{2}eydy$$
$$e^4/2-2e$$

 

[nameVoid]

...?

 

[╔(σ_σ)╝]

What is your question?
What you have done seems to make mathematical sense assuming your limits of integration is correct .

 

[nameVoid]

the problem directly from the text reads int int e^(x/y) dA, 1<=y<=2 , y<=x<=y^3 shows a solution of 6