Consider the definite integral

$\int^2_1(4x^2+2x+6)dx$

Let I_e be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is I_s. The percentage error is defined as e = 100 × (I_e - I_s)/I_e The value of e is

Numerical integration using trapezoidal rule gives the best result for a single variable function, which is

The root of the function $$f\left( x \right) = {x^3} + x - 1$$ obtained after first iteration on application of Newton-Raphson scheme using an initial guess of $${x_0} = 1$$ is

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