Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

Please help me regarding this!

share|cite|improve this question
All you have are coordinates of your points? You can use the trapezoidal rule for starters... – J. M. 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.

share|cite|improve this answer
...and this is in fact the trapezoidal rule. – J. M. Aug 14 '12 at 11:31

This is the formula you are looking for I suppose:


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

share|cite|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.