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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 for Area under the Curve

\[\LARGE Area = \int_{a}^{b}f(x)dx\]

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 ?

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

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

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

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

$\large = 18$

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