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

The formula for Area under the Curve  = ab f(x)dx

Solved Example

Question : 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

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

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

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

= [(42 – 8)/3] – [(1 – 21)/3]

= (34 + 20)/3
= 54/3

= 18 sq.units

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