# How do i solve this with trapezoid rule?

#### paschim

Q: [FONT=&quot]Evaluate [/FONT][FONT=&quot] using Trapezoidal rule with h = 0.2. Hence determine the value of π.

I missed quite a few classes due to sickness when they explained this stuff, and now with the report submission deadline rushing in, I really need this solved.

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#### Also sprach Zarathustra

Hello!

Use this "formula":

$$\displaystyle \int\limits_a^b \approx \frac{b-a}{n}[\frac{f(x_0)+f(x_n)}{2}+f(x_1)+f(x_2)+\dots+f(x_{n-1})]$$

Your $$\displaystyle h$$ is $$\displaystyle \frac{b-a}{n}$$.

This can be easily proved if you take your section $$\displaystyle /[a,b]$$ and dividing him to $$\displaystyle n$$ equal parts, and then taking the trapezes to evaluate the integral.

• paschim

#### paschim

Thanks, but how do I find the value of PI? Where does the PI come from in this equation?

#### Also sprach Zarathustra

hey...

Thanks, but how do I find the value of PI? Where does the PI come from in this equation?
$$\displaystyle \int\limits_0^1{\frac{1}{1+x^2}}dx=\arctan(1)-\arctan(0)=\frac{\pi}{4}$$