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!
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!
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.
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.