Application of Integrals
There are various Applications of Integrals in mathematics. Some are mentioned below:
- It is used to calculate the area under simple curves.
- Find areas enclosed by lines, arcs of circles, parabolas, ellipses.
- Find out the centroids of areas of Triangle with curved boundaries.
- Find out the area between two curves and more.
How to Find Area Between Curve and Axis?
We can find the Area between a curve y = f(x), the x-axis, and specific intervals that is the lines x = a and x = b by using integration:
∫ab y.dx = ∫ab f(x).dx = F(b) -F(a)
Similarly, when dealing with the region enclosed by the curve x= g(y), the y-axis, and the lines y = a and y = b, the Integral expression is:
∫ab x.dy = ∫ab g(y).dy = G(b) -G(a)
How to Find Area Between Two Curve?
For areas between two curves y = g(x) and y = f(x), where f(x) ≥ g(x) in the interval [a, b], the area between x = a and x = b is:
∫ab f(x).dx – ∫ab g(x).dx = ∫ab {f(x) – g(x)}.dx
Similarly, for regions between two curves x = g(y) and x = f(y), where f(y) ≥ g(y) in the interval [c, d], the Integral expression becomes:
∫ab f(y).dy – ∫ab g(y).dy = ∫ab {f(y) – g(y)}.dx
Learn more about, Area Between Two Curves.
How to Find Area Under Curve?
To calculate the Area under a Curve, follow the steps added below
- Step1: Firstly identify the equation of the curve y=f(x), the limits and the axis for area calculation.
- Step2: The integration (antiderivative) of the curve is found.
- Step3: The upper and lower limits are applied to the integral result, and the difference gives the area under the curve:
Area = ∫ab y.dx
⇒ Area = ∫ab g(x).dx
⇒ Area = [g(x)]ba
Area = g(b) − g(a)
Application of Integrals
Application of Integrals are used to find the area and volume of various 2-D and 3-D curves and they have vast applications in the fields of mathematics and physics. They generally help us to calculate the area of the curve, irregular contour, the volume of various curves, and others.
In this article, we will discuss Applications of Integral and its meaning. We will also understand its application and formulae to calculate the Integral value in mathematics. We will also solve various examples and provide practice questions for a better understanding of the concept of this article. We have to study the Application of Integrals in Class 12.
Table of Content
- Application of Integral in Mathematics
- Types of Integrals
- Application of Integrals
- Application of Integrals in Physics
- Examples on Applications of Integrals
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