Integrals Class 12 CBSE Maths Chapter 7

Class 12 CBSE Maths Syllabus
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 11:3D Geometry
Chapter 12: Linear Programming
Chapter 13: Probability

Introduction

We have provided a few important points that are covered in NCERT Class 12 Maths Chapter 7 Integrals to help students in their exam preparations. Refer to the points below:

Integration is the inverse process of differentiation. In differential calculus, we are given a function and we have to find the derivative or differential of this function, but in integral calculus, we are to find a function whose differential is given. Thus, integration is a process which is the inverse of differentiation.

Fundamental Integration formulas:
- ∫ xⁿdx = x⁽ⁿ⁺¹⁾/(n+1) + C , ∀n ≠ −1
- ∫ x⁻¹dx = ∫ 1/x dx = log |x| + C
- ∫ e^xdx = e^x + C
- ∫ a^xdx = a^x/log a + C
- ∫ logx dx = xlogx − x + C
First fundamental Theorem of Integral Calculus:
- Let f be a continuous function of x for a ≤ x ≤ b and A(x) = ∫^x_af(x) dx, then A′(x) = f(x) for all x in [a, b] and A(a) = 0.
Integration by parts: The integral of the product of two functions = first function × integral of the second function – integral of {differential coefficient of the first function × integral of the second function}. Care must be taken in choosing the first function and the second function. Obviously, we must take that function as the second function whose integral is well known to us.