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 _________.

During the numerical solution of a first order differential equation using the Euler (also known as Euler Cauchy) method with step size $$h,$$ the local truncation error is of the order of