Area Under Curve

Define Area Under a Curve.

Region enclosed by the curve, the axis, and the boundary points is referred to as the area under the curve. Using the coordinate axes and the integration formula, the area under the curve has been determined as a two-dimensional area.

How to Calculate Area Under a Curve?

There are three methods to find area under the curve, that are:

• Reimann Sums involve dividing the curve into smaller rectangles and adding their areas, with the number of subintervals affecting the precision of the result.
• Definite Integrals are similar to Reimann Sums but use an infinite number of subintervals to provide an exact result. 
• Approximation Methods is used known geometric shapes to approximate the area under the curve.

What is Difference Between a Definite Integral and a Reimann Sum?

Key difference between a definite integral and a Reimann Sum is that a definite integral represents the exact area under a given curve whereas a Reimann Sum represents the approximate value of the area and the accuracy of the sum depends upon the chosen partition size.

Can Area Under Curve be Negative? 

If curve is below axis or lies in the coordinate axis’s negative quadrants, the area under the curve is negative. In this case as well, the area under the curve is computed using the conventional approach, and the solution is then modulated. Even in cases when the answer is negative, just the area’s value is taken into account, not the answer’s negative sign.

What does Area Under Curve Represent in Statistics?

Area under curve(ROC) is the measure of the accuracy of a quantitative diagnostic test.

How do you Interpret Sign of Area Under a Curve?

Sign of area shows that area under curve is above x-axis or below x-axis. If area is positive, then area under curve is above the x-axis and if it negative then area under curve is below x-axis.

How is Area Under Curve Approximated?

By segmenting the region into tiny rectangles, the area under the curve may be roughly estimated. And by adding the areas of these rectangles, one may get the area under the curve.

Area Under Curve is area enclosed by curve and the coordinate axes, it is calculated by taking very small rectangles and then taking their sum if we take infinitely small rectangles then their sum is calculated by taking the limit of the function so formed.

For a given function f(x) defined in the interval [a, b], the area (A) under the curve of f(x) from ‘a’ to ‘b’ is given by A = ∫_a ^b f(x)dx. The area under a curve is computed by taking the absolute value of the function over the interval [a, b], summed over the range.

In this article, we will learn about, the area under the curve, its applications, examples, and others in detail.