Antiderivatives Class 11 Mathematics Solutions | Exercise - 18.6
Chapter - 18
Antiderivatives
An important aspect of calculus in class 11 is antiderivatives, which are used to calculate areas under curves, evaluate indefinite integrals, and solve differential equations. Antiderivatives can be used to find the area under a curve, evaluate integrals, and solve differential equations. Through integration by substitution, integration by parts, and trigonometric substitution, students learn how to calculate antiderivatives.
It is also taught how to calculate antiderivatives using the Fundamental Theorem of Calculus. Additionally, students are taught how to find the antiderivative of a function as well as how to measure definite integrals using the substitution rule for integrals.
We shall now proceed to the solution section after we have had a little idea about antiderivatives and some of the subtopics relating to antiderivatives, as well as some of the typical formulas that make up an antiderivative.
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.
Definite Integral as an Area under the given curve
In The definite integral of a function f(x) is the area under the curve of f(x) between two points a and b. This area can be expressed as an integral, which is a calculus concept that allows us to calculate the area under a curve. It is calculated by taking the integral of the function between the two points of interest.
In the case of a definite integral, the area is bounded by a specific function and two points, typically a and b. The definite integral is then expressed as an expression of the form:
\int_a^b f(x) \, dx
This expression can be evaluated to calculate the area under the curve of f(x) between the two points a and b.
Exercise - 18.6
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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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sir there's not the solution after no. 5 please update soon