The integral $$\,\,\oint\limits_C {\left( {ydx - xdy} \right)\,\,} $$ is evaluated along the circle $${x^2} + {y^2} = {1 \over 4}\,$$ traversed in counter clockwise direction. The integral is equal to

In the following table, $$x$$ is a discrete random variable and $$p(x)$$ is the probability density. The standard deviation of $$x$$ is

If $$\,y = f\left( x \right)\,\,$$ is the solution of $${{{d^2}y} \over {d{x^2}}} = 0$$ with the boundary conditions $$y=5$$ at $$x=0,$$ and $$\,{{dy} \over {dx}} = 2$$ at $$x=10,$$ $$f(15)=$$_______.

Using the trapezoidal rule, and dividing the interval of integration into three equal sub-intervals, the definite integral $$\,\,\int\limits_{ - 1}^{ + 1} {\left| x \right|dx\,\,} $$ is