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 = ∫ab f(x)dx
Question : 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
= [(42 – 8)/3] – [(1 – 21)/3]
= (34 + 20)/3
= 18 sq.units