English Guide: Practical Tips for Better English Communication

misused words literally In our last blog, we discussed words that are commonly misused in English. In this article, we will add some more words that are commonly misused. Knowing the correct usage will help you to enhance your vocabulary as well as spoken English Skills which will help you to speak effectively. Let us look at the words.10 words with incorrect usage1. An effectAn effect means either to influence or to fake whereas to effect means to put into effect.Examples:The new...
you can do it In life, there are many situations which make us sad and feel low. At that moment when someone encourages us with their positive words, we feel light and happy.  Don’t we? We encourage people playing sports, while building relationships with friends, family, colleagues, and while working. In the same manner, when your friend or your loved one feels low, you try to encourage them with positive words by complimenting and appreciating them. In...
give it a shot In our last blog, we taught you few phrases that can be used for encouraging someone. When you use these phrases in your communication, it not only helps you to motivate someone but also improves your English-speaking skills. Let’s have a look at some positive phrases that will improve your English skills and help you encourage someone.6 phrases you must know1. You are almost there!This phrase is best to encourage someone who is about to...
interjections In our earlier blog, we provided a fun guide to interjections which help us in our day to day conversation. Interjections are words for the emotions and expressions that we make. These interjections words depict our emotions like surprise, agreement, disagreement, sarcasm, shock etc. In today’s blog, we will explain interjections to be used to express your emotions which will help you in your everyday conversations using “expressive...
couch potato Idioms play an important role in English language. They help to express your feelings in a figurative manner. In today’s lesson, we will describe people and their characteristics with idiomatic expressions. These people might be your friends, cousins, co-workers and to some your family members. All these characters are different from each other and have a unique differentiating factor through which we identify or know them. Let us learn the...
relationships February is a month of love and people all over the world celebrate their relationships. While not everyone might be in a relation, but everyone might surely be aware of relationships. Today’s English lesson will provide you with some phrases which are used in English communication while conversing about relationships.7 vocabulary terms to talk about relationships1. Long distance relationshipMeaning - A relationship where the two people who are in...
compliment man Women get compliments more often for their looks, smile, the way they walk or talk etc. However, it’s not always that women get compliments; men too get compliments. Men also like to get compliments. Who doesn’t like to get praised for their appearance? As a small gesture, you can compliment them on their appearance – it might be their new hairstyle, beard, moustache etc. The only thing to remember here is to use adjectives like cool, handsome, trendy,...
misused words Words have the tendency to make or break the sentence. When a word is used correctly, it makes a wonderful meaningful sentence. In the same way when the word is wrongly used it creates a wrong sentence. Generally, it happens with non-native English speakers. However, practising these words and knowing their appropriate meaning will help with its correct usage. So, in this article, we are bringing words that are confused and misused.9 words...
you are right A conversation is incomplete without a set of questions. It doesn’t matter with whom you are talking, but it will surely have a question. For e.g. while commuting, if a co-passenger asks whether it’s a Chicago-bound train and you confirm it by replying yes to him. There are many instances when you will have to reply to someone that they are correct. In today’s blog, you will learn English phrases that can be used to agree with someone or to say...
act your age Age is something that is never shared and asking a girl or a woman her age, is considered bad manners. People rarely talk about their age and salary. Although, while conversing in English, people refer to idioms related to age to give a hint about their age,no one wants to reveal their actual age and want to be referred to as a sweet sixteen. Sweet sixteen is regarded as the characteristic age of prettiness and innocence in a girl. In today’s...
article thumbnailLife is full of surprises and shocks. You might never know when a surprise can turn into a shock. There are many times when we warn people to avoid taking too many risks or if they are climbing up a ladder you might warn them to be safe. Sometimes we see formal notices, pictures, posters that act as warnings about dangers. For e.g. If someone is investing all his money in stock market, you might warn them to avoid taking too many risks or...
article thumbnailYou know it's the last month of the year, and you are in celebration and vacation mood. And not to forget, the favorite season, winter. Who doesn’t like winter or let’s say who doesn’t like to sit indoors by the fireside in the mornings and evenings with a hot cup of tea. We all love it. With a week or a few days away from Christmas and New Year, we are already in party mood. People visit their family and friends to spend their time and enjoy...
article thumbnailIn our last blog, we listed five holiday idioms that described the holiday. In today’s blog, we will discuss few more idioms and phrases that are related to holidays. Most of the people in foreign countries use holiday phrases and idioms while conversing in English. So, having a fair knowledge about these with their meaning will come handy when you are on a vacation.5 Holiday phrases and idioms1. Let your hair down Meaning - to allow yourself to...
article thumbnailhttp://eagetutor.com/December is that time of the month when many countries are in a festive mood. Christmas and New Year bring holidays and celebration mood along with them. In many English-speaking countries, they send gifts and greetings to wish their friends and family. If you are planning a vacation in any of the countries especially in December, then knowing some holiday greetings might surely help you. Even if you don’t celebrate...
article thumbnailHair is the personality of a person, especially women. It makes them look beautiful. Everyone has a unique hairstyle which makes their appearance different. While some flaunt it, others nag about it. Whatever you do, you express it with words and phrases. These expressions are nothing but idioms and phrases. These idioms have a figurative meaning. Let us learn some expressions about hair that is generally used by a native speaker.Must know...
article thumbnailMany times in life, we find people who poke their nose in every matter. They are curious to know everything that happens in our life. Sometimes it becomes difficult to avoid these people as they might be our friend or a close relative. We don’t like to answer each question. So, in today’s blog, we are bringing you some English phrases which will help you avoid answering an unwanted question.6 phrases to be used1. (Sorry) That’s personalThis phrase must...
article thumbnailPhrasal verbs are a combination of words which consist of a verb and a preposition or a combination of verb and adverb. When these words are combined, they usually give a different meaning. Knowingly or unknowingly, we are using some common phrasal verbs in our day to day life. To know and understand those common phrasal verbs we are here to help you out. Today, we will provide you phrasal verbs that are used in our day to day life.10 daily...
article thumbnailAdjectives are words that describe nouns or give information about the noun. A native English speaker uses various adjectives while communicating in English. Using adjectives in a sentence means enhancing the language by making it interesting. In our day to day life, we use many adjectives while speaking and writing in English. For e.g. If someone asks, how are you? You say, I am fine or I am doing good. However, an English learner would use...
article thumbnailIn our recent blog, we listed vocabularies related to beach, sea, and ocean. Today, we will explain expressions and idioms related to the sea. May it be a beach, ocean, or a sea, who doesn’t love spending time and relaxing there. Many times, when you are with your colleagues over a casual chat, you might have heard idiomatic expressions that are figurative in nature. For e.g. It is raining cats and dogs. However, this sentence means it's...
article thumbnailIn our last blog, we explained about idioms and expressions related to ocean and sea. This blog will help you learn some more idioms which will improve your English communication. Let’s have a look at these idioms.9 must know idioms1. Take sand to the beachMeaning – A pointless or useless activityE.g. Why don’t you understand, hiring a cab for 5 minute distance is like taking sand to the beach.2. Drink like a fishMeaning – When someone...
article thumbnailWho doesn’t love spending time on the beach? Summer is the perfect time to hit the beach. The warm weather gives a perfect reason to visit the beach and get some cool breeze. People visit the beach for various reasons. If you happen to get a chance to visit a beach especially in a foreign country, then don’t miss this opportunity. The beaches there are very different. Before you hit the beach learn some beach vocabulary that would help to...
article thumbnailFood is something that everyone loves. Thinking of food itself makes us hungry. If you are a food lover and have a knack for cooking, then you might have surely tried many food items. Your culinary skills would make you a cooking expert or you might even land to Master Chef. Although your cooking skills may possibly give you a new job, but average or poor communication skills may ruin your chance. The way you talk, the way you present or you...
article thumbnailIn our last blog, we explained a few beach vocabulary words. People visit beaches for various purpose. Some go for adventure while others go for relaxing their mind. No matter what the reason is, if you are visiting the beach, knowing these words will help you while conversing with a native speaker.Must know beach vocabulary words1. ShoreShore is the area where sand meets the ocean or sea.2. SandbarWhen the force of the water pushes the...
article thumbnailIn English language, we have words to describe every particular thing in this world. May it be a person or an animal, we have names for every species. Although, when it comes to gender, many people find it difficult to understand the noun gender. So, in this blog, we will explain gender nouns for all English learners.Types of gender nouns There are four types of gender nouns which will be explained below:1. Masculine genderWe say a noun is a...
article thumbnailIn life, there are times when we face situations where we lose our loved ones or near and dear ones. It might be anyone from our friend’s family or our family or even a pet. The loss is huge which can’t be replaced in any manner. Generally, people don’t understand what to say or how to console the person. The words might fall short when you try to give condolences to the bereaved. If you happen to come under such unexpected situations, then try...




introductiontointegration1Calculus is centered on the concept of the derivative.  If a function ‘f’ is differentiable in an interval I, then its derivative f’ exists at each point of I.  We can think about the question, if f’ exists at each point of I then what will be the function? Such functions are called anti-derivatives.  The formula that gives all these anti-derivatives is called the indefinite integral of the function and the process of finding anti-derivatives is called integration.  The development of integral calculus arises out of the efforts of solving the problems of the following types:
i)    The problem of finding a function whenever its derivative is given.
ii)    The problem of finding the area bounded by the graph of a function under certain conditions.
These two types of problems lead to indefinite and definite integrals, which together constitute the Integral Calculus.

Integration as an Inverse Process of Differentiation

Integration is the inverse process of differentiation.  If we are given the derivative of a function and asked to find its primitive (original function), the process is called integration or anti-differentiation.
Let us consider few examples,
i)    d (tanx)  = sec2x                  …………….(1)

The function sec2x is the derived function of tanx, so we say that tanx is the anti-derivative of sec2x
ii)    d (logx) =  1
      __           ___
      dx            x                        ……………..(2)  

The function 1/x is the derived function of logx, so we that logx is the           anti-derivative of 1/x.
We know that the derivative of any real number C, treated as a Constant Function is zero. And hence we can write (1) and (2) as
         d (tanx+ C)= Sec2x        d(logx +C) = 1
        __                               ___             __
        dx                                dx               x

Hence the anti-derivatives (integrals) given above are not unique.  There exists infinitely many integrals of each these functions which can be obtained by choosing C arbitrarily from the set of real numbers.  Hence C is referred to as arbitrary constant.
In general, if there is a function F such that d F(x) = f(x) for all xЄI then for any arbitrary real number C,                                __           

                               d [F(x)+C] = f(x), x Є I

We introduce the new symbol, ∫f(x) dx which will represent the entire class of anti derivatives read as the indefinite integral of ‘f’ w. r. t x.
Symbolically, we write ∫f(x) dx = F(x) + C
f(x) in ∫f(x)dx is the integrand, ‘x’ in f(x) is the variable of integration, ‘C’ is the constant of integration.

Geometrical interpretation of indefinite integral

The statement ∫f(x) dx=F(x) + C=y, represents a family of curves.  The different values of C will correspond to different members of this family and these members can be obtained by shifting any one of the curves parallel to itself.  This is the geometrical interpretation of indefinite integral.

Some properties of indefinite integral

1)    The process of differentiation and integration are inverses of each other which results in
                 ∫f’(x)dx=f(x)+C, where C is any arbitrary constant.
2)    Two indefinite integrals with the same derivative lead to the same family of curves and so they are equivalent.
Let ‘f’ and ‘g’ be two functions such that
                    d ∫f(x) dx= d ∫g(x) dx
                   __             __                  
                   dx             dx

3)    ∫[f(x)+g(x)]dx = ∫f(x)dx + ∫g(x)dx
4)    For any real number ‘k’, ∫k f(x) dx= k ∫f(x) dx
5)    Properties 3 and 4 can be generalized to a finite number of functions f1, f2 ……….. fn and the real numbers k1, k2…………kn giving
∫ [k1f1(x) + k2f2(x) +…..+ knfn(x)] dx = k1∫f1(x)dx + k2∫f2(x)dx +       …….+kn∫fn(x)dx.

Comparison between differentiation and integration

1.    Both are operations on functions.
2.    Both satisfy the property of linearity.  For any two constants k1 and k2,
a)    d[k1f1(x)+k2f2(x)] = k1d[f1(x)] + k2 d[f2(x)]
      __                            __               __   
      dx                            dx                dx

b)    ∫[k1f1(x)+k2f2(x)] dx= k1∫f1(x) dx + k2∫f2(x)dx
3.    All the functions are not differentiable, in the same way all the functions are not integrable.
4.    The derivative of a function if it exists, is unique, but the integral of a function is not unique.
5.    The derivative of a polynomial function is a polynomial function with power less than one, but the integral of a polynomial function is a polynomial function with power more than one.
6.     We can find derivative at a point, but the integral of a function exist only for an interval not at a point.
7.    The geometrical meaning of a derivative is that it is the slope of tangent to a corresponding curve at a point but the geometrical meaning of an indefinite integral is a family of curves placed parallel to each other having parallel tangents at the points of intersection of the curves of the family with the lines orthogonal to the axis representing the variable of integration.

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