Question

explain integration by partial functions.....​

Answer 1

Answer:

Integration by Partial Fractions: We know that a rational function is a ratio of two polynomials P(x)/Q(x), where Q(x) ≠ 0. Now, if the degree of P(x) is lesser than the degree of Q(x), then it is a proper fraction, else it is an improper fraction.

Answer 2

Step-by-step explanation:

Integration by Partial Fractions: We know that a rational function is a ratio of two polynomials P(x)/Q(x), where Q(x) ≠ 0. Now, if the degree of P(x) is lesser than the degree of Q(x), then it is a proper fraction, else it is an improper fraction. Even if a fraction is improper, it can be reduced to a proper fraction by the long division process.

• Browse more Topics Under Integrals
• Fundamental Theorem of Calculus
• Introduction to Integration
• Properties of Indefinite Integrals
• Properties of Definite Integrals
• Definite Integral as a Limit of a Sum
• Integration by Partial Fractions
• Integration by Parts
• Integration by Substitutions

Integral of Some Particular Functions

Integral of the Type e^x[f(x) + f'(x)]dx

So, if P(x)/Q(x) is an improper fraction, then P(x)/Q(x) = T(x) + P1(x)/Q(x) … where T(x) is a polynomial and P1(x)/Q(x) is a proper rational fraction. We already know how to integrate polynomials and in this article, we will be learning about integration by partial fractions. Also, the rational functions that we will consider are those whose denominators can be factorised into linear and quadratic equations.