URGENT !!! need help with these 3 integrals problems

[reverie414]

Hi, I need urgent help with these 3 integrals problems ... been stuck on the questions and the deadline is Friday. Thanks a lot !


1) For the green's theorem,

I got the answer : 18.684. Not sure whether it is correct. Please kindly explain in steps so I know where I went wrong.


2) I'm totally unsure about finding the surface integral. How do I know the shape of the surface ?

3) and finding the curl function f

All I know is, it has something to do with curl. Something like F = grad f.


Thanks again !

 

[galactus]

1) For the green's theorem,

I got the answer : 18.684. Not sure whether it is correct. Please kindly explain in steps so I know where I went wrong.

\(\displaystyle \L\\\int\int\left[\frac{\partial}{\partial{x}}ye^{x}-\frac{\partial}{\partial{y}}xln(y)\right]dA=\int_{0}^{3}\int_{1}^{2}(e^{x}y-\frac{x}{y})dydx=\frac{3e^{3}}{2}-\frac{9ln(2)}{2}-\frac{3}{2}\approx{25.51}\)

 

[reverie414]

1) For the green's theorem,

I got the answer : 18.684. Not sure whether it is correct. Please kindly explain in steps so I know where I went wrong.

\(\displaystyle \L\\\int\int\left[\frac{\partial}{\partial{x}}ye^{x}-\frac{\partial}{\partial{y}}xln(y)\right]dA=\int_{0}^{3}\int_{1}^{2}(e^{x}y-\frac{x}{y})dydx=\frac{3e^{3}}{2}-\frac{9ln(2)}{2}-\frac{3}{2}\approx{25.51}\)

Hi, thanks for replying. This is what I got, e^3(y^2/2)|2,1 - 9/2ln(y)|2,1 = 27.552. Erm, where did I go wrong ?