Methods in which we reduce the function standard forms for finding the integrals are:
a) Integration by parts
b) Integration using partial fraction
c) Integration by substitution
d) All the above
Answer
300.3k+ views
Hint: Check every method and observe if the given method is capable of reducing the integral function into standard form so that it can be solved. If after altering the integral function using respective methods can be solved then it must be the method of reduction of function into standard form.
Complete step-by-step answer:
Integration by part, integration using partial fraction, integration by substitution are used to reduce the function into integrals as:
In integration by part,
$\int {uvdx\; = u\int {vdx\; - \int {u\prime (\int v dx)dx} } } $
We reduce the two-function consisting equation into standard form.
Integration using partial fraction,
It’s used when fraction is in improper form and we can convert into proper fraction using this method.
Integration by substitution,
In this method we use when the integrand consists of two functions in the expression and one function is derivative of the other.
$\int {uv\;dx} $, such that $\dfrac{{du}}{{dx}} = v$
Hence, the correct option is (d).
Note: We have to check which operation reduces the expression in standard form. We should know how to use the operations to find the same like for Integration by parts solving, ILATE method gives an idea for choosing functions.
Complete step-by-step answer:
Integration by part, integration using partial fraction, integration by substitution are used to reduce the function into integrals as:
In integration by part,
$\int {uvdx\; = u\int {vdx\; - \int {u\prime (\int v dx)dx} } } $
We reduce the two-function consisting equation into standard form.
Integration using partial fraction,
It’s used when fraction is in improper form and we can convert into proper fraction using this method.
Integration by substitution,
In this method we use when the integrand consists of two functions in the expression and one function is derivative of the other.
$\int {uv\;dx} $, such that $\dfrac{{du}}{{dx}} = v$
Hence, the correct option is (d).
Note: We have to check which operation reduces the expression in standard form. We should know how to use the operations to find the same like for Integration by parts solving, ILATE method gives an idea for choosing functions.
Recently Updated Pages
Letfx be a polynomial with positive degree satisfy-class-12-maths-JEE_Main

Evaluate the definite integral given as intlimits13left class 12 maths JEE_Main

The sum of squares of two parts of a number 100 is-class-12-maths-JEE_Main

The HCF of two numbers is 96 and their LCM is 1296 class 10 maths JEE_Main

If the magnetizing field on a ferromagnetic material class 12 physics JEE_Main

Four persons A B C and D initially at the corners of class 11 physics JEE_Main

Trending doubts
JEE Main 2026: Exam Dates, Session 2 Updates, City Slip, Admit Card & Latest News

Understanding the Electric Field of a Uniformly Charged Ring

Electron Gain Enthalpy and Electron Affinity Explained

Derivation of Equation of Trajectory Explained for Students

Understanding Atomic Structure for Beginners

How to Convert a Galvanometer into an Ammeter or Voltmeter

Other Pages
JEE Advanced Percentile vs Marks 2026: JEE Main Cutoff, AIR & IIT Admission Guide

Hybridisation in Chemistry – Concept, Types & Applications

Effective Nuclear Charge for JEE

Understanding the Angle of Deviation in a Prism

Degree of Dissociation: Meaning, Formula, Calculation & Uses

JEE Advanced Weightage Chapter Wise 2026 for Physics, Chemistry, and Mathematics

