Rs Aggarwal Class 12 Integration using Partial Functions PDF

Rs Aggarwal Class 12 Integration using Partial Functions PDF

Welcome to sidclasses.in. Here we have provided RS Aggarwal Class 12 Integration using Partial Functions PDF which you can download very easily. Rs Aggarwal is a mathematics book based on NCERT with lots of questions to practice. If you have cleared your concept from NCERT maths book class 12 then now it’s time for you to go for the question of RS Aggarwal Class 12 Integration using Partial Functions PDF.

Integration using partial fractions is a method used to evaluate integrals of rational functions, which are functions in the form of a fraction of polynomials. The method of partial fractions is based on the fact that any rational function can be expressed as the sum of a polynomial and a sum of simpler fractions called partial fractions.

What are Partial Functions in Integrals?

The general process of using partial fractions to evaluate an integral is as follows:

  1. Write the rational function in the form of a fraction.
  2. Factor the denominator of the fraction into its irreducible factors.
  3. Express the numerator as the sum of a polynomial and a sum of simpler fractions.
  4. Integrate each of the simpler fractions separately.
  5. Integrate the polynomial.
  6. Add the results of steps 4 and 5 to obtain the antiderivative of the original function.

For example, consider the integral of (x^2 – 1)/(x^3 – x^2 – x + 1)dx.

  1. Write the fraction in standard form: (x^2 – 1)/(x^3 – x^2 – x + 1) = (x^2 – 1)/((x-1)(x^2+x+1))
  2. Factor the denominator: (x^2 – 1)/((x-1)(x^2+x+1))
  3. Express the numerator as the sum of a polynomial and a sum of simpler fractions. (x^2 – 1) = A(x-1) + B(x^2+x+1)
  4. Integrate each of the simpler fractions separately. A(x-1) dx = A x dx – A dx and B(x^2+x+1) dx = Bx^2 dx + Bx dx + B dx.
  5. Integrate the polynomial. x^2 dx = (x^3)/3 + C
  6. Add the results of steps 4 and 5 to obtain the antiderivative of the original function. (A x dx – A dx) + (Bx^2 dx + Bx dx + B dx) + (x^3)/3 + C

By doing this process one can find the antiderivative of the function without knowing the original function.

It’s important to note that this method can be a bit tricky and may require the use of algebraic manipulation, especially when the denominator of the function is not easily factorable.

Ch-15-Integration-Using-Partial-Fraction

Rs Aggarwal Class 12 PDF (All Chapters PDF)

Chapter no.chapter namepdf
1RelationsDownload
2FunctionsDownload
3Binary OperationsDownload
4Inverse Trigonometric FunctionsDownload
5MatricesDownload
6DeterminantsDownload
7Adjoint and Inverse Of MatrixDownload
8System of Linear EquationsDownload
9Continuity and DifferentiabilityDownload
10DifferentiationsDownload
11Applications of DerivativesDownload
12Indefinite IntegralsDownload
13Methods of integrationDownload
14Some Special integralsDownload
15Integration using Partial FunctionsDownload
16Definite integralsDownload
17Area of Bounded RegionsDownload
18Differential equations and their formationsDownload
19Differential equations with variable separableDownload
20Homogeneous Integral equationsDownload
21Linear Differential equationsDownload
22Vectors And Their PropertiesDownload
23Scalar, or Dot product of VectorsDownload
24Cross or vector products of VectorDownload
25Product of three vectorsDownload
26Fundamental Concepts of 3D GeometryDownload
27Straight Line in SpaceDownload
28The PlaneDownload
29ProbabilityDownload
30Bayes’s Theorem and its ApplicationsDownload
31Probability DistributionDownload
32Binomial DistributionsDownload
33Linear ProgrammingDownload

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