Important Integration Formulas for Jee

In calculus, integration plays a crucial role, especially in JEE exams. Mastering the fundamental integration formulas ensures that students can solve complex problems efficiently. This blog covers a list of all integral formulas that are essential for JEE, along with their examples to help you understand their applications better.

1.0Introduction to Integration

Integration is the inverse process of differentiation. If a F(x) is the integral of f(x), then F'(x) = f(x). It helps in finding the area under a curve, volumes, and solving differential equations, which are important in physics and mathematics.

Integration of Rational Function:                                   

(i) A rational function is defined as the quotient of two polynomials, expressed in the form

$\frac{P(x)}{Q(x)}$​, where P(x) and Q(x) are polynomials in x and Q(x) ≠ 0. If the degree of P(x) is less than the degree of Q(x), the rational function is classified as proper. Conversely, if the degree of P(x) is greater than or equal to the degree of Q(x), it is termed improper. An improper rational function can be transformed into a proper rational function through the process of long division.

Thus, if a rational function is improper, it can be expressed as:

$\frac{P(x)}{Q(x)}=H(x)+\frac{R(x)}{Q(x)}$​,

where H(x) is a polynomial and $\frac{R(x)}{Q(x)}$​ is a proper rational function. To simplify the integration of such functions, we use a technique known as partial fraction decomposition, which breaks the integrand into a sum of simpler rational functions. Once decomposed, the integral can be evaluated easily using standard integration methods.