Rs Aggarwal Class 12 Methods of integration PDF
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What are the methods of Integration?
There are several methods of integration that can be used to find the antiderivative of a function, including:
- The power rule: This method is used for integrals of the form ∫x^n dx, where n is a constant. The result is given by x^(n+1) / (n+1) + C.
- The substitution method: This method is used when the original integral is difficult to evaluate directly. It involves making a substitution of the variable of integration to simplify the integral.
- Integration by parts: This method is used when the integral is a product of two functions, such as ∫u(x)v'(x) dx. The result is given by u(x)v(x) – ∫v(x)u'(x) dx.
- Trigonometric identities: This method is used to evaluate integrals of form ∫f(x)sin(x) dx or ∫f(x)cos(x) dx.
- Trigonometric substitution: This method is used to evaluate integrals that involve the square root of a quadratic function.
- Partial fractions: This method is used when the integrand is a rational function, i.e. a function in the form of a fraction of polynomials
- Tables of integrals: This method is used for commonly encountered functions, such as ∫e^x dx or ∫1/x dx.
These are some of the basic and most used methods in integration.
It’s important to note that, sometimes no matter which method you use, you may not be able to find an explicit solution, in this case, one can use numerical methods to calculate the integral.
CH-13-Methods-of-integrationRs Aggarwal Class 12 PDF (All Chapters)
| Chapter no. | chapter name | |
|---|---|---|
| 1 | Relations | Download |
| 2 | Functions | Download |
| 3 | Binary Operations | Download |
| 4 | Inverse Trigonometric Functions | Download |
| 5 | Matrices | Download |
| 6 | Determinants | Download |
| 7 | Adjoint and Inverse Of Matrix | Download |
| 8 | System of Linear Equations | Download |
| 9 | Continuity and Differentiability | Download |
| 10 | Differentiations | Download |
| 11 | Applications of Derivatives | Download |
| 12 | Indefinite Integrals | Download |
| 13 | Methods of integration | Download |
| 14 | Some Special integrals | Download |
| 15 | Integration using Partial Functions | Download |
| 16 | Definite integrals | Download |
| 17 | Area of Bounded Regions | Download |
| 18 | Differential equations and their formations | Download |
| 19 | Differential equations with variable separable | Download |
| 20 | Homogeneous Integral equations | Download |
| 21 | Linear Differential equations | Download |
| 22 | Vectors And Their Properties | Download |
| 23 | Scalar, or Dot product of Vectors | Download |
| 24 | Cross or vector products of Vector | Download |
| 25 | Product of three vectors | Download |
| 26 | Fundamental Concepts of 3D Geometry | Download |
| 27 | Straight Line in Space | Download |
| 28 | The Plane | Download |
| 29 | Probability | Download |
| 30 | Bayes’s Theorem and its Applications | Download |
| 31 | Probability Distribution | Download |
| 32 | Binomial Distributions | Download |
| 33 | Linear Programming | Download |