Antiderivatives Class 11 Mathematics Solutions | Exercise - 18.2
Chapter - 18
Antiderivatives
Students in class 11 learn about a type of calculus called antiderivatives. Antiderivatives are used to calculate the area under the curve of a function, evaluate an integral that has an indefinite value, and solve differential equations. In this course, students learn how to calculate antiderivatives utilizing the methods of integration by substitution, integration by parts, and trigonometric substitution.
Additionally, the student will learn how to calculate antiderivatives using the Fundamental Theorem of Calculus. In addition, the student will learn how to identify a function's antiderivative and use the substitution rule to evaluate definite integrals from the Fundamental Theorem of Calculus.
So before moving on to the solution section, let us have a little idea about those antiderivaties and the subtopics that are related to these derivatives, as well as some of the most important formulas that are used in them.
Introduction
Antiderivatives, also known as indefinite integrals, are the inverse operation of derivatives. In other words, an antiderivative is the original function from which a derivative was derived.
For example, the derivative of f(x) = x² is f'(x) = 2x. Therefore, the antiderivative of 2x is f(x) = x². Antiderivatives can be used to find the area under a curve, and can also be used to solve differential equations.
Integration by Substitution Method
In the preceding section we have seen that integrals can be integrated easily when they are in standard forms. A given integral may not always be in a standard form. So to reduce it to a standard form we have to change the variable into a new one by a suitable substitution. To make a proper choice one must have a lot of practice and skill. At the time of substitution, we express the given function x in term of the new variable y (say) and replace dx by (dy)/(dx)×dx.
Exercise - 18.2
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Is Class 11 Mathematics Guide Helpful For Student ?
I have published this Notes for helping students who can't solve difficult maths problems. Student should not fully depend on this note for completing all the exercises. If you totally depend on this note and simply copy as it is then it may affect your study.
Student should also use their own will power and try to solve problems themselves. You can use this mathematics guide PDF as a reference. You should check all the answers before copying because all the answers may not be correct. There may be some minor mistakes in the note, please consider those mistakes.
How to secure good marks in Mathematics ?
As, you may know I'm also a student. Being a student is not so easy. You have to study different subjects simultaneously. From my point of view most of the student are weak in mathematics. You can take me as an example, I am also weak in mathematics. I also face problems while solving mathematics questions .
If you want to secure good marks in mathematics then you should practise them everyday. You should once revise all the exercise which are already taught in class. When you are solving maths problems, start from easy questions that you know already. If you do so then you won't get bored.
Maths is not only about practising, especially in grade 11 you to have the basic concept of the problem. When you get the main concept of the problem then you can easily any problems in which similar concept are applied.
When your teacher tries to make the concept clear by giving examples then all students tries to remember the same example but you should never do that. You can create your own formula which you won't forget later.
If you give proper time for your practise with proper technique then you can definitely score a good marks in your examination.
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Sanjeev
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Very helpful. Thank you very much brother ❤