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. 


read more

Teaching Your Child About Internet Safety

School children will begin to learn about the internet and its benefits, but also its drawbacks. Young children are also vulnerable and will need to learn about the risks of being on the internet. Teach your child early on about being safe on the internet with this guide from this prep school in the South West.

The first conversations

The age for children to be using the Internet decreases as time goes by, as we’re entering a new era of accessibility in technology for children. The key thing to remember is that you should show your willingness to be interested in what they’re doing both online and offline.

Show them that you know what they’re interested in and how they can access information around their favourite things online. This can be as simple as showing them how to use a search engine, or how to play with apps on a smartphone or tablet.

Listen to your child and understand why they want to use the internet and for what purpose. As your child grows older they will come to rely on the internet for further study advice and support, especially during exam periods. They may also want to chat with friends online by playing games or video calls to support their learning.

Warning them of the risks

Child safety is critical when allowing your child to use the internet and is the most concerning element of allowing them free reign. This discussion should be had with your child before they use the computer to go online.

The main risks children could face are:

  • Cyberbullying
  • Phishing
  • Downloading viruses without their knowledge
  • Indecent conversations
  • Viewing explicit content
  • Providing sensitive information to strangers

For parents there should be a series of restrictions in place for your child to avoid accessing indecent websites, social media (until they’re old enough), and ways they could be caught by viruses or phishing software. A lot of internet packages now provide this service.

Tell your child why you do this and they’ll learn how to find those signs if they’re navigating the internet. They’ll soon begin to understand what’s right and what’s wrong when it comes to using online services.

Showing them how to be resilient

The key message for children is to identify what parts of the internet are problematic and what they need to do if they find inappropriate content online.

When they’re younger it’s wise to oversee what websites they’re visiting and what they’ll be using the internet for. Show them the key indicators that a website is safe and let them have a look at a website and identify features that they think are safe or harmful.

There’s a whole range of content online that children, as they grow, will want to be interested in. Their favourite hobbies, online services and communities are accessed using the internet that won’t be avoided – it’s just showing them how to act when they find something rude or uncomfortable. They’ll learn to be resilient and know how to action content when they see it, or know when to talk to an adult about what they have found.

read more