Applications of Integrals
This chapter included topics like how to find the area of different geometrical figures such as circles, parabolas, and ellipses. The area enclosed by the curve y = f (x); x-axis and the lines x = a and x = b (b > a) is given by the formula,
- Area = ∫bay.dx =∫baf(x).dx
Area of the region bounded by the curve x = φ (y) as its y-axis and the lines y = c, y = d is given by the formula:
- Area = ∫dcx.dy = ∫dcϕ(y).dy
The area enclosed in between the two given curves y = f (x), y = g (x), and the lines x = a, x = b is given by the following formula:
- Area = ∫ba[f(x)−g(x)].dx, {where, f(x) ≥ g(x) in [a,b]}
If f (x) ≥ g (x) in [a, c] and f (x) ≤ g (x) in [c, b], a < c < b, then the resultant area between the curve is given as,
- Area=∫ca[f(x)−g(x)].dx, + ∫bc[g(x)−f(x)].dx
Class 12 Maths Formulas
Class 12 maths formulas page is designed for the convenience of the learners so that one can understand all the important concepts of Class 12 Mathematics directly and easily. Math formulae for Class 12 are for the students who find mathematics to be a nightmare and difficult to grasp. They may become hesitant and lose interest in studies as a result of this. We have included all of the key formulae for the 12th standard Maths topic, which students may simply recall, to assist them in understanding Maths in a straightforward manner. For all courses such as Integration, Differentiation, Trignometry, Relation and Functions, and so on, the formulae are provided here according to the NCERT curriculum.
Table of Content
- Chapter 1: Relations and Functions
- Chapter 2: Inverse Trigonometric Functions
- Chapter 3: Matrices
- Chapter 4: Determinants
- Chapter 5: Continuity and Differentiability
- Chapter 6: Applications of Derivatives
- Chapter 7: Integrals
- Chapter 8: Applications of Integrals
- Chapter 9: Differential Equations
- Chapter 10: Vector Algebra
- Chapter 11: Three-Dimensional Geometry
- Chapter 12: Linear Programming
- Chapter 13: Probability
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