Maths Application of Integrals Formulas: Almost half of the CBSE Class 12 mathematics subject is composed of calculus. Both differentiation and integration concepts feature heavily in the curriculum, along with their applications.
Chapter 8 Application of Integrals is one of the shortest but still important chapters in Class 12 mathematics. It builds on the previous chapter of Integrals and focuses on their applications to find areas of curves, planes etc.
The application of Integrals has been revised as per the new rationalized NCERT books, which are prescribed by the Central Board of Secondary Education (CBSE). As such, students have to learn fewer concepts than their counterparts in pre-covid times.
However, today we cover the formulas and important definitions of the Application of Integrals. These can benefit you in higher studies and other subjects like physics as well. You can check out all the CBSE Class 12 Maths Chapter 8 Application of Integrals Formulas, present and deleted here.
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We have listed all the important formulas, definitions and properties of CBSE Class 12 Application of Integrals here.
What are Applications of Integrals?
In geometry, we learn the formulas and methods to calculate areas of various figures like triangles, rectangles, trapezes and circles. Such formulae are fundamental in the applications of mathematics to many real life problems.
The formulae of elementary geometry allow us to calculate areas of many simple figures. However, they are inadequate for calculating the areas enclosed by curves. For that we need the help of some concepts of Integral Calculus.
Areas Under Simple Curves
The area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) is given by the formula:
The area of the region bounded by the curve x = φ (y), y-axis and the lines y = c, y = d is given by the formula:
Formulas from Deleted Syllabus
The below formulas are from deleted topics from the CBSE 12th Chapter 8 Application of Integrals but can benefit high-achievers or students who are preparing for entrance exams.
The area of the region enclosed between two curves y = f (x), y = g (x) and the lines x = a, x = b is given by the formula,
If f (x) ≥ g (x) in [a, c] and f (x) ≤ g (x) in [c, b], a < c < b, then
Also Read
CBSE Class 12 Maths Syllabus 2023-24
CBSE Class 12 Maths Sample Paper 2023-24
NCERT Solutions for Class 12 Maths PDF
