Evaluate $\iint_{R} (2x - y)\,dA$, where $R$ is the triangle with vertices $(0,0),(3,0),(0,3)$.

Which iterated integral equals $\iint_R f(x,y)\,dA$ where $R=\{(x,y): y=x^2,\ y=\sqrt{x}\}$?

For the transformation $u=x^2+y^2,\ v=\arctan\!\left(\tfrac{y}{x}\right)$ with $x>0$, compute $\left|\dfrac{\partial(x,y)}{\partial(u,v)}\right|$.

Evaluate $\oint_C \mathbf{F}\cdot d\mathbf{r}$ for $\mathbf{F}=\langle -y,\ x^2\rangle$ and $C$ the unit circle (CCW).

For $\mathbf{F}=\langle yz,\ zx,\ xy\rangle$, compute $\nabla\times\mathbf{F}$ at $(1,-1,2)$.

Evaluate $\iiint_{x^2+y^2\le 1,\ 0\le z\le 3} z\, dV$ using cylindrical coordinates.

For $\mathbf{F}=\langle 3x^2+y,\ x+2y\rangle$, compute $\int_C \mathbf{F}\cdot d\mathbf{r}$ from $(1,0)$ to $(2,1)$ (any path).

Find the area enclosed by $y=4-x^2$ and $y=x$.

Let $C$ be the boundary of the unit square $[0,1]\times[0,1]$ (CCW). For $\mathbf{F}=\langle xy,\ x - y\rangle$, compute $\oint_C \mathbf{F}\cdot d\mathbf{r}$.

Choose correct limits for $\iiint_R 1\,dV$ where $R$ is the solid between the paraboloid $z=x^2+y^2$ and the plane $z=4$.