Area Under Curve Formulae
Formula for various types of calculation of Area Under Curve is tabulated below:
Type of Area | Formula of Area |
|---|---|
| Area Using Riemanns Sum | [Tex]\bold{Area = \sum_{i=1}^{n}f(x_i)\Delta x_i}[/Tex] |
| Area with Respect to y-axis | [Tex]\bold{A = \int_{a}^{b}f(y)dy}[/Tex] |
| Area with respect to x-axis | [Tex]\bold{A = \int_{a}^{b}f(x)dx}[/Tex] |
| Area under Parabola | 2∫ab√(4ax).dx |
| Area under Circle | 4∫ab√(a2 – x2).dx |
| Area under Ellipse | 4b/a∫ab√(a2 – x2).dx |
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Area Under 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.
Table of Content
- What is Area Under Curve?
- Calculating the Area Under the Curve
- Using Reimann Sums
- Using Definite Integrals
- Approximating Area Under Curve
- Calculating Area Under Curve
- Area Under Curve Formulae