1pt) let f(x, y)=−yi+xjx2+y2 and let c be the circle r(t)=(cost)i+(sint)j, 0≤t≤2π. a. compute ∂q∂x= note: your answer should be an expression of x and y; e. g. "3xy−y" b. compute ∂p∂y= note: your answer should be an expression of x and y; e. g. "3xy−y" c. compute ∫cf⋅dr= note: your answer should be a number d. is f conservative? type y if yes, type n if no.

What are and supposed to be? Can't answer a/b without that information.

I'll come back to part (c) in a moment. If we can show is conservative, this part will be a breeze.

For part (d), to show whether is conservative, we have to show that there is a scalar function such that . It appears that you've written



I'm not sure what to make of the that follows. means that




Integrating the first PDE with respect to gives



Differentiating with respect to gives




But we assumed that is a function of alone, which means there is no solution for , and therefore no solution for . Hence is not conservative.

Back to part (c). is not conservative, so we have to compute the line integral the "long" way. Replacing and , we have