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.

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 – 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

\begin{array}{l} A r e a = \int_{- 1}^{2} (7 - x^{2}) d x \end{array}

\begin{array}{l} = (7 x - \frac{1}{3} x^{3}) |_{- 1}^{2} \end{array}

\begin{array}{l} = [7.2 - \frac{1}{3} (8)] - [7 (- 1) - \frac{1}{3} (- 1)] \end{array}

= [(42 – 8)/3] – [(1 – 21)/3]

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

= 18 sq.units

Area under the Curve Formula

Formula to Calculate the Area Under a Curve

Solved Example

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