# Tag Info

Accepted

• 2,967

### Evaluate the line integral $\int_{L} \frac{-y \,d x+x \,d y}{x^{2}+y^{2}}$ for a line segment $L$

The "change in argument" is, informally, just the total net angle that the path winds around the origin anticlockwise (a negative change in argument indicates a net clockwise winding). We ...
• 82.6k

### $\iint_Sz^2d\sigma$ where $S$ is an area of the cone $z=\sqrt{x^2+y^2}$ between planes $z=0$ and $z=1.$

The factor $\sqrt2$ arises from the area element of the given cone $$dS = \sqrt{1+( z_x’)^2+ ( z_y ’)^2} \ dxdy= \sqrt2\ dxdy$$
• 67.3k
Accepted

### $\iint_Sz^2d\sigma$ where $S$ is an area of the cone $z=\sqrt{x^2+y^2}$ between planes $z=0$ and $z=1.$

The problem in your approach is the fact $\displaystyle \iint_{S}f(x,y,z)\, {\rm d}\sigma$ is a surface integral. You don't have $\displaystyle \iint_{D}f(x,y)\, {\rm d}A$ that is a double integral in ...
• 2,366