Education

Integration – Important Things to Know

Students who dream to pursue their engineering in IITs and NITs should clear the JEE main exam. Every year, this exam is conducted by NTA. Since a huge number of students appear for this exam, the competition level is high. Proper preparation and planning is very important to crack this exam and gain a seat in prestigious engineering institutions. To have a thorough knowledge of Maths is very important to easily score high ranks in this exam. 

The JEE main exam paper 1 consists of 90 questions. 25 questions each from Physics, Chemistry, and Mathematics. Students have to attempt only 75 questions. There will be 20 multiple choice questions and 10 numerical questions from each subject. Students need to attempt only 5 out of 10 numerical questions. As far as the JEE exam is concerned, definite and indefinite integration is an important topic. Students can expect 3 questions from this topic. Following are the important topics in mathematics.

  • Calculus
  • Coordinate geometry
  • 3D Geometry and vectors
  • Algebra
  • Trigonometry

Integration and differentiation are two most important topics in calculus. Differentiation is a process of finding a function that outputs the rate of change of one variable with respect to another variable. The reverse of differentiation is integration. Students are recommended to have a clear understanding of both integration and differentiation so that they can easily solve the problems related to these topics. There are many formulas in integration and differentiation. To solve the problems at a higher speed, learning these formulas is very important.

Important formulas for indefinite integration

Following are some important formulas for indefinite integration.

  1. ∫ex dx = ex + c
  2. ∫ax dx = ax/ln a + c
  3. ∫xn dx = (xn+1/(n+1)) + c
  4. ∫1/x dx = log x + c
  5. ∫sin x = -cos x + c
  6. ∫cos x = sin x + c
  7. ∫sec2x = tan x + c

Here c denotes the constant of integration. Following are some methods of integration. They are By parts method, substitution method, reduction method, Euler substitution, and integration by partial fractions. 

 

Integration by parts

This is a special method of integration that is useful when two functions are multiplied together. Let u and v be two functions. We consider u as the first function and v as the second function. Then the integral of u.v is given by

∫u.v dx = u∫v dx – ∫u’ ∫(v dx) dx

= first function. ∫second function – ∫ derivative of first function.∫ second function

JEE Main Integration previous year solved problems

Students are recommended to practice previous year question papers. A number of previous year questions are available online. Students can easily access and download them. They can easily download and practice JEE Main Integration previous year solved problems from BYJU’S website. They can save the PDFs for offline use. Practising these questions will help them to analyze their level of knowledge in each topic. They can compare their answers with the solutions provided. It will also help them to increase their speed of solving problems and confidence. 

 

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