Area Under the Curve Formula

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.

Area under the Curve Formula

Formula to Calculate the Area Under a Curve

Formula for Area under the Curve Area = ∫ab f(x)dx

Solved Examples

Question 1: Calculate the area under the curve of a function, f(x) = 7- x2, the limit is given as  x = -1 to 2 ?
Solution:

Given function is, f(x) = 7- x2 and limit is x = -1 to 2

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

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

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

$\large = 18$


Practise This Question

Which of the following are correct about physisorption?

1) Decrease in entropy of system
2) Decrease in enthalpy
3) The value of TdS is positive
4) It is reversible in nature