# How to calculate the area of a graph when $x$ and $y$ values are given?

I have $x$ and $y$ values and I need to calculate the area of the graph with those $x$ and $y$ values.

How can I calculate that?

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All you have are coordinates of your points? You can use the trapezoidal rule for starters... –  Guess who it is. Aug 14 '12 at 11:11

Say you have a function $f(x)$, and a set of domain values $\{a= x_0,x_1,x_2,\ldots,x_n=b\}$, where $x_{i+1}>x_i$. The points $x_i$ partition the $x$-axis into a discrete set of subintervals $L_i = [x_i,x_{i+1}]$. You can approximate the area between the function and the $x$-axis for a given subinterval by the following formula (the trapezoid rule):

$$A_i = |L_i|\times \frac{f(x_i)+f(x_{i+1})}{2},$$

where $|L_i|=x_{i+1}-x_i$ is the length of the subinterval. The total approximated area between $a$ and $b$ is just the sum of all the areas,

$$A=\displaystyle\sum_{i=0}^{n-1} A_i.$$

You can find an interactive demo of the trapezoid rule here. Loosely speaking, the greater the value of $n$ the better the approximation of the area.

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...and this is in fact the trapezoidal rule. –  Guess who it is. Aug 14 '12 at 11:31

This is the formula you are looking for I suppose:

$$\text{Area}=\int_{a}^{b}{f(x)\:dx},$$

Where $a$ and $b$ are your limits of integration and $f(x)$ is the function of the graph.

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hi thank you can u plz tell me how to calcute with that formaula? I am new to derivatives and integrals... –  Sivani Aug 14 '12 at 11:09