The area under a curve between two points is found out by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a & x = b, integrate y = f(x) between the limits of a and b. This area can be calculated using integration with given limits.

## Formula to Calculate the Area Under a Curve

The formula for Area under the Curve = **∫**_{a}^{b} f(x)dx

### Solved Example

**Question : **Calculate the area under the curve of a function, f(x) = 7 – x^{2}, the limit is given as x = -1 to 2.

** Solution:**

Given function is, f(x) = 7- x^{2} and limit is x = -1 to 2

$\large Area = \int_{-1}^{2}(7-x^{2})dx$

$\large = \left ( 7x-\frac{1}{3}x^{3}\right)|_{-1}^{2}$

$\large = \left [ 7.2-\frac{1}{3}(8) \right ]-\left [ 7(-1)-\frac{1}{3}(-1)\right ]$

= [(42 – 8)/3] – [(1 – 21)/3]

= (34 + 20)/3

= 54/3

= 18 sq.units