[13.3] - Think before you compute

1. Compute $\int_C (ye^{xy}\uv i + xe^{xy}\uv j)\cdot d\myv r$ for the curve $C$ shown below.
   
   
2. Compute $\int_C (yz^2\uv i + xz^2\uv j+2xyz\uv k)\cdot d\myv r$ for the curve $C$ shown below.
   
   
3. Let $\myv F(x,y)=(2x+y)\cos(x^2+xy)\uv i+\left(x\cos(x^2+xy)+1\right)\uv j$.
   1. Show that $\myv F$ is a conservative vector field.
   2. Let $C$ be the curve parameterized by $\myv r(t)=\sin t\uv i+(1-\cos t)\uv j$ with $0\leq t\leq \pi$.
      Find $\int_C \myv F \cdot d\myv r$.