Numerical Methods - Integration

The exact solution of $\int_0^4 \frac{dx}{1+x}$ is represented as n. If m represents numerically evaluated value of the above integral using Trapezoidal rule by considering four equal subintervals in the range of x, then...

The values of a function f obtained for different values of x are shown in the table below. Using Simpson's one-third rule, $\int_0^1 f(x) dx \approx$ ________ (rounded off to 2 decimal places).

Value of $\int_{4}^{5.2} \ln x \, dx$ using Simpson's one-third rule with interval size 0.3 is

P (0, 3), Q (0.5, 4), and R (1, 5) are three points on the curve defined by $f(x)$. Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits $x = 0$ and $x = 1$ for the curve. The...