Evaluate the integral

I=∫_0^2π▒〖Cos² xdx〗

Using the following methods with 6 evaluations:
Trapezoidal rule
Simpson's 1/3 rule
Simpson's 1/8 rule
Gauss-Legendre quadrature formula

Could you retype your problem without using copy paste from a document?

Something like this:

Int ^2_0 (function) dx

First of all, Thank you very much for your kind reply.
The question is:

Evaluate the integral I= Int ^0_2pi ( ( Cos^2) x )dx
Using the following methods with 6 evaluations:
(a) Trapezoidal rule
(b) Simpson's 1/3 rule
(c) Simposn's 1/8 rule
(d) Gauss-Legendre quadrature formula

Thank you again.

(a) With 6 intervals, you get the trapezium height as \frac{\pi}{3}

So, find the points on the graph at pi/3 intervals.

1. 0 --> cos^2(0) = 1
2. pi/3 --> cos^2(pi/3) = 0.25
3. 2pi/3 --> cos^2(2pi/3) = 0.25
4. pi --> cos^2(pi) = 1
5. 4pi/3 --> cos^2(4pi/3) = 0.25
6. 5pi/3 --> cos^2(5pi/3) = 0.25
7. 2pi --> cos^2(2pi) = 0.25

Then, evaluate, with 6 intervals;

\int^{b}_a f(x) dx \approx \frac12 \(d)(y_6 + y_0 + 2(y_1+y_2+y_3+y_4+y_5))

\int^{2\pi}_0 \cos^2\ x\ dx \approx \frac12 \(\frac{\pi}{3}\)(1 + 0.25 + 2(0.25+0.25+1+0.25+0.25))

Sorry, for the others, I don't know those approximations... :(