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What Are The Concepts Of Integration And Differentiation? How To Calculate?




The integration and differentiation both are the basic concept of calculus and together form, “the first fundamental theorem of calculus”. The integral and differential calculus both hold a remarkable place in the calculus and form separate disciplines.

The differential calculus subfield deals with derivatives of a function. It studies how changes occur in certain quantities considering the function derivatives. A functions’ graph can be calculated, evaluated, and estimated through differentiation.

Integral calculus forms the second branch of the calculus. Composing the concept of antiderivative, integration is the inverse of differentiation. The area under a curve can be successfully found using the integration.

Let us learn more about integration and derivatives and how we can calculate them, considering the article below.

What are the Basic Concepts of Integration

The algebraic method of finding the integral of a function at any point on the graph is known as the process of integration. To find the integral of a function with respect to a particular variable x, we use the Leibniz formula. It represents the area computation for the x-axis of the curve.

As mentioned above, the integration can also be called the antiderivative, as differentiation and integration are reverse processes of each other. While derivatives give you rate of change at any moment, integrals give you the exact distance at a specific time. Inverse and the area of a curve are computed using integrals.

One alternative approach to look at an integral is to consider it to be the “area under a curve”. This area may be either definite integral or indefinite integrals. The definite integrals give a result, in contrast to an indefinite integral (represented as the formulas) as a number that reflects the area. An indefinite integral has no limits or bounds, while a definite integral has limits of integration.Definite integrals and indefinite integrals are slightly different concepts and their formulas are different. You can find definite integrals and indefinite integrals by using online definite integration calculator and indefinite integration calculator.

How to Calculate Integration

To calculate the integral of a function the most fundamental approaches for integration include the integration by substitution, integration by parts and integration using partial fractions.

The integral of function can be calculated by one or combining these techniques where applicable. Let us have a closer look at these techniques separately to find the integral of a function.

By substitution

Substitution method is one of the main techniques to calculate integration. An integral of the type is an example upon which the substitution method is implied. The integral may sometimes become a type suited for another technique by use of substitution t = g(x).

By Partial Fraction

The technique of partial fraction to calculate integration is implied if the integrand is a rational function (a polynomial being divided by a polynomial). In such a case the substitution method cannot be used and the denominator can be determined by linear or/or quadratic factors.

By Parts

Integration by parts techniques is implied in order to calculate integral when the integrand is a product of one integrable and one differentiable function. However, except when the integrand is In(x), it may be expressed as the product of two functions represented as In(x) = 1 x In(x).

The Basic Concept of Differentiation

The algebraic technique for computing derivatives of a function is termed as the process of differentiation. Whereas the slope or gradient at any point on a graph is known as the derivative of a function.

The value of the tangent drawn to that curve at any given point forms the gradient of a curve.

The derivative of a function is also described as changing a building in relation to a change in the unit of another building.

If f(x) be a separate variable x function. Then in the independent variable x, for a tiny change, Δx is caused. In function f(x) a corresponding change Δ f(x) occurs. The ratio then is denoted as:


The expression above denotes a measure of the rate of change of f(x) in relation to x.

How to Calculate Derivative of a Function

To perform the differentiation process or calculate the derivative of a function, the notation used can be calculated as, if f is a function having a real value and a is any point in its field where f is defined, f(x) is said to be differentiable in point x=a if f'(a) is present in its domain at all points then

f(a) =

Since that limit exists, f'(a) is the f(x) derivative at a. This is the initial principle in order to calculate derivatives. Moreover, the f'(a) domain is defined in presence of its bounds/limits, then the derivative can also be denoted as

d/d(x), f(x) or D(f(x))

Again, the derivative of f(x) is represented then as d/dx or y’ if y = f(x), this expression is stated as derivative of y with respect to x. And the derivative of function f in x at x = a is represented by

d/dx f(x)|x=a or df/dx|x=a

Thus, the derivative of a function f(x) denotes the rate of change of the function f(x) with respect to x at a point belonging to its domain. For a function to be differentiable at any point x = a in its domain, it must be continuous at that specific point but vice-versa is necessarily not always true.

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How Should I Prepare For SUPER TET And CTET Simultaneously





Every year, Uttar Pradesh and the CBSE board arranges the CTET examination for aspiring candidates who want to teach primary and secondary candidates. However, the examination preparation procedure is quite easy and similar to each other. Here are some tips that you can use to simultaneously prepare for the SUPER TET and CTET.

Solve The Previous Year Question Papers

It is one of the essential preparation tips that you need to keep in mind when preparing for the SUPER TET and CTET examinations. Both the examinations have huge competitions. Solving previous years question papers for Super TET and CTET will help you provide a clear idea regarding the questions. Along with that, you will be able to find about the various methods about solving them. Moreover, it is important to understand that solving these helps develop the right strategies to clear the SUPER TET and CTET examinations.

Find Out Your Performance.

Once you have solved the question, make sure that you check your overall performance. For example, find out where you are going wrong and the mistakes you made. Also, it will become easy for you to know about the areas where you are doing good. If you want, you can keep practicing the maximum number of question papers since it will help in enhancing your performance. These things are quite beneficial, especially if you want to score well in the exam and clear it in one go.

Maintain Regular Practicing

CTET Mock tests as well as for Super TET and previous year’s questions are quite useful and if you want to remove any errors. With regular practice, you will become confident. Besides, adhering to solving the papers will help in making you aware of time. Moreover, time sense is extremely important when appearing for competitive exams. Focus on solving simple questions since the competitive examinations mostly opt for simple questions. Make sure that you are regularly practicing the questions.

Focus On Accuracy As Well As Attempt

Since most of the competitive examinations like SUPER TET and CTET do not have any negative marking, it is still necessary to maintain accuracy. Make sure that you are attempting the questions correctly. At first, checkout the topics where you can attempt all the questions without making any mistakes. Do not forget to mark the questions regarding which you were not sure about. Attempt those in the last, especially if you have extra time. However, make sure that you are crossing the passing marks so that you can get a better ranking among the other competitors.

Prioritizing The Subjects Is Necessary.

Even though it is extremely important to score good in every subject, you should have a clear idea about the examination pattern. Therefore, focus on the subjects and give time to those in which you are good. But, before that, you must know the examination pattern. Once you find out the pattern, it will become easy for you to attempt the questions without making any mistakes.

Teaching Method Is Important.

It is vital to check the teaching method for which you can refer to guidance of experts available at BYJU’s Exam Prep. Although the competitive examination is all about self-studying, but sometimes taking tuitions turn out to be useful. Check whether the teacher you chose focuses on the preparation tactics and makes you practice the previous year’s question. These things are essential when preparing for the SUPER TET and CTET. Also, ask your tutor to hand over important notes that are useful for clearing the exam.

Hence, if you appear for the SUPER TET and CTET, you can use these tips simultaneously for clearing the exam.


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Best Hotel Management Institute in Lucknow



Hotel Management Institute in Lucknow

The Best Hotel Management Institute in Lucknow is UEI Global, Lucknow. It is a private college that is affiliated to Manglayatan University, which is also known for its quality education. The campus is a world-class facility with separate hostels for girls and boys. It has excellent infrastructure, placement statistics, and scholarships. The best hotel management institute in India is UEI Global, which has received prestigious rankings and offers several awards.

UEI Global provides an undergraduate degree in hospitality and tourism. The college provides separate hostels for boys and girls, wi-fi connectivity on campus, and separate housing facilities for boys and girls. Students should have a minimum of 55% marks in 10+2 to be considered for admission to the institute. The Amity chain has numerous branches across India, and its reputation is unmatched for its excellent infrastructure and placement statistics.

There are also scholarship opportunities. The best hotel management institute in Lucknow is the one that offers the most desirable placement packages. The institute has internship partners like Pizza Hut and KFC. The placement packages at these schools are also among the best in the country. You can apply for a hotel management job in the renowned companies in Lucknow with the help of these institutes.

The UEI Global campus is located in Gomti Nagar and is close to Pickup Bhawan. Its faculty is highly qualified and experienced and aims to prepare students for the international market. The students will get a hands-on experience in a real hotel. The course syllabus is structured to provide the most relevant knowledge of hotel management. They will learn how to handle a hotel as an employee, as well as the business operations that make the hotel successful.

The IHM Lucknow offers an average package but the UEI Global offers a higher price package. These are the two best hotel management institutes in Lucknow. If you are planning to pursue an MBA in Hospitality, it is important to choose the right hotel management institute. The right education is crucial for the success of your career. You can easily get a high-quality education from a reputed Hotel Management Institute in Lucknow.

UEI Global offers an accredited program that prepares students for the hospitality industry. UEI Global training program is designed for the global market. It also focuses on core areas that are essential for a successful hotel. The IHM is the best option for those who want to pursue an MBA in hospitality. The IHM course is accredited by the UGC and is the best way to get an MBA. It helps you to learn the intricacies of the hospitality industry and to become an asset for the future.

Besides offering diploma courses, UEI Global is also the best Hotel Management Institute in Lucknow. It offers diploma courses in food production, bakery and confectionery, and food & beverage service. UEI Global is the most modern Hospitality & Management Institute in Lucknow and is the best hotel management institute in Lucknow.

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Why Take a Hotel Management Course?



Hotel Management Course

You can earn your Hospitality Management and Tourism degree by enrolling in an accredited University college that specializes in the field. You can also complete a degree from a business school with a relevant department. Whatever your reason for enrolling in a Hospitality Management and Tourism course, there is a program for you. A degree in this area is an excellent way to enter the hospitality industry. Regardless of where you’re looking for your education, you can find it online.

The eighth module will focus on the importance of situational awareness. This type of awareness is essential to ensure that your hotel is meeting the highest quality standards possible. You must be able to anticipate problems before they happen to ensure that they don’t affect your guests. During the training, you’ll also be exposed to real-life situations so that you can prevent them from happening. The best way to prepare for these challenges is to take a Hotel Management Course.

Once you’ve completed your course, you’ll need to learn how to handle guest complaints. It’s essential to understand that hotel guests have different needs and requirements, and the staff must be able to identify these needs. By learning to observe small differences, you’ll be better equipped to provide the best possible service. You’ll also learn the basics of bookkeeping and accounting, which is important for the hospitality industry. Ultimately, a Hospitality Management course will help you navigate the intricacies of hotel operations and ensure that your hotel meets customer expectations.

There are many advantages to studying Hospitality Management. Apart from the obvious benefits of having an MBA, this will also boost your resume. In addition to enhancing your professional qualifications, specialized training will give you the edge in the interview process. Taking a Hotel Management Course will not only benefit your career, but it will also increase your earning potential. So, if you’re thinking about taking a degree in this field, you can get started now. You’ll soon find yourself at a level of responsibility and success, and you’ll find yourself in a high-paid position.

A hospitality management course will give you the tools to succeed in your chosen career. After completing the course, you’ll have the opportunity to manage a large hotel or run your own. Once you’ve got the experience, you’ll be able to open your own business. Your salary will be high, but you can choose to take an internship in the field that interests you the most. If you’re passionate about running a successful hotel, this may be the right course for you.

Whether you’re interested in becoming a restaurant manager, hotel executive, or chef, a hospitality course will help you find a job you’re passionate about. The hospitality industry is full of exciting careers, and the right Hotel Management course can lay the foundation for your future. Luckily, you can find hundreds of different opportunities in the hospitality industry by studying at a university. And the benefits are endless: With a degree in Hospitality, you can work as a food and beverage manager, a bartender, or a chef, and more. You can also become a wine expert.

While a hospitality industry can be extremely competitive, a career in this field requires an analytical mindset. A hotel management course will prepare you for the challenges of the hospitality industry. During the two-year duration of a graduate course, you’ll learn the various elements of the hospitality industry and how to make the most of your potential in the field. You’ll gain a valuable insight into all aspects of the hotel and how to meet customers, make decisions, and manage a successful hotel.

A Hotel Management Course is designed to prepare candidates for a career in the hospitality industry. Students will learn about human resources and how to develop flexible employees. In addition, you’ll gain a comprehensive understanding of the hotel management industry by taking an MBA. It’s a rewarding career choice that can help you advance your education and your professional goals. With a Bachelor’s Degree in Business Administration, you can get an understanding of the fundamentals of management and pursue your dreams.

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