Numerical Integration

For the integral ${\int }_0^{\pi /2}\left(8+4\cos x\right)dx$, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the endpoints, is _____ 

(round off to one decimal place0.

Torque exerted on a flywheel over a cycle is listed in the table. Flywheel energy (in J per unit cycle) using Simpson's rule is

By Simpsons' $\frac{1}{3}rd$ rule, the value of ${\int }_1^7\frac{dx}{x}$ is

For the data,

$\begin{array}{cc}x:& 0 1 2\\ f\left(x\right):& 8 5 6\end{array}$

the value of ${\int }_0^2{\left[f\left(x\right)\right]}^{2}dx$ by Trapezoidal rule will be:

Considering four subintervals, the value of ${\int }_0^1\frac{1}{1+x}dx$ by Trapezoidal rule is:

Trapezoidal rule for the evaluation of ${\int }_a^{b}f\left(x\right)dx$ requires the interval $\left[a,b\right]$ to be divided into:

Trapezoidal Rule gives exact values of the integral when the integrand is a

Consider the below data:

$\begin{array}{ccccc}x& :& 0& 1& 2\\ f\left(x\right)& :& 4& 3& 12\end{array}$

The value of ${\int }_0^{2}f\left(x\right)dx$ by Trapezoidal rule will be:

The integral ${\int }_1^{10}{x}^{3}dx$ is approximately evaluated by Trapezoidal rule ${\int }_1^{10}{x}^3 dx$ $=3\left[\frac{1+{10}^3}{2}+\alpha +7^3\right]$ for$n=3$, then the value of $\alpha$ is

With the help of Trapezoidal rule for numerical integration and the following table

the value of ${\int }_0^{1}f\left(x\right)dx$ is

Calculate by Trapezoidal rule an approximate value of ${\int }_{-3}^3{x}^{4}dx$ by taking seven equidistant ordinates

Which of these methods for numerical integration is also called as parabolic formula?
 

A curve is drawn to pass through the points given by the following table.

Using Simpson's $1/3 rd$  rule, estimate the area bounded by the curve, the$x-$axis and the lines $x=1, x=4$

The value of ${\int }_0^{1}xdx$ by Trapezoidal rule taking $x=4$ is

By Simposon's rule taking $n=4$, the value of the integral ${\int }_0^1\frac{dx}{1+x^2}$ is equal to

Using trapezoidal rule and taking $n=4$, the value of ${\int }_0^2\frac{dx}{1+x}$ will be

If $e^0=1,e^1=272,e^2=7.39,e^3=20.09$ $e^4=54.60$, then the value of ${\int }_0^4{e}^{x}dx$ using Simpson's rule, will be

The value of $f\left(x\right)$ is given only at $x=0,\frac{1}{3},\frac{2}{3},1$. Which of the following can be used to evaluate${\int }_0^{1}f\left(x\right)dx$ approximately?

According to Simpson's rule, the value of ${\int }_1^7\frac{dx}{x}$ is

By Simpson's $\frac{1}{3}rd$ rule, the approximate value of the integral ${\int }_1^2{e}^{-x/2}dx$ using four intervals, is