To solve the equation $$2sinx=x$$ by Newton- Raphson method, the initial guess was chosen to be $$x=2.0.$$ Consider $$x$$ in radian only. The value of $$x$$ (in radian) obtained after one iteration will be closest to

In numerical integration using Simpson's rule, the approximating function in the interval is a

Using the Simpson's $$1/{3^{rd}}$$ rule, the value of $$\,\int {ydx} \,\,$$ computed, for the data given below, is

If the equation $$sin(x)$$ $$\, = {x^2}$$ is solved by Newton Raphson's method with the initial guess of $$x=1,$$ then the value of $$x$$ after $$2$$ iterations would be _________.