Mathematics Exam > Mathematics Videos > Calculus > Substitution Rule for Indefinite Integrals
Substitution Rule for Indefinite Integrals Video Lecture | Calculus - Mathematics
|
112 videos|65 docs|3 tests
|
FAQs on Substitution Rule for Indefinite Integrals Video Lecture - Calculus - Mathematics
| 1. What is the substitution rule for indefinite integrals? |  |
Ans. The substitution rule, also known as the u-substitution method, is a technique used to evaluate indefinite integrals. It involves making a substitution by introducing a new variable, typically denoted as u, which allows us to simplify the integral and make it easier to solve.
| 2. How does the substitution rule work? | |
Ans. The substitution rule works by replacing the original variable in the integral with the new variable u. This substitution is chosen in such a way that it simplifies the integral and allows us to integrate it easily. After the substitution, we differentiate u with respect to the original variable and replace any remaining instances of the original variable with u. Finally, we integrate the resulting expression with respect to u and then substitute back the original variable if needed.
| 3. When should I use the substitution rule for indefinite integrals? | |
Ans. The substitution rule is particularly useful when dealing with integrals that involve compositions of functions, exponential functions, or trigonometric functions. It can also be used when the integrand contains a radical or a product of functions that can be simplified through substitution. If you encounter an integral that seems difficult to evaluate directly, trying the substitution rule is often a good strategy.
| 4. What are the steps involved in applying the substitution rule? | |
Ans. The steps for applying the substitution rule are as follows:
1. Identify a suitable substitution by selecting a new variable u.
2. Compute du/dx, the derivative of u with respect to the original variable x.
3. Replace all instances of the original variable x in the integral with the new variable u.
4. Replace dx with du in the integral.
5. Simplify the integral as much as possible using the substitution.
6. Integrate the resulting expression with respect to u.
7. Substitute back the original variable if necessary.
| 5. Can you provide an example of how to use the substitution rule for indefinite integrals? | |
Ans. Sure! Let's consider the integral ∫(2x + 1)² dx. To solve this integral, we can use the substitution rule. Let's make the substitution u = 2x + 1.
Differentiating u with respect to x gives du/dx = 2. Rearranging this equation, we have dx = du/2.
Substituting these values into the integral, we get ∫(2x + 1)² dx = ∫u² * (du/2).
Simplifying this expression, we have 1/2 ∫u² du.
Integrating u² with respect to u gives (1/2) * (u³/3) + C, where C is the constant of integration.
Finally, substituting back the original variable, we have (1/2) * ((2x + 1)³/3) + C as the solution to the original integral.
Related Exams
About this Video
|
4.75/5 Rating |
|
Dec 24, 2024 Last updated |
Video Description: Substitution Rule for Indefinite Integrals for Mathematics 2024 is part of Calculus preparation.
The notes and questions for Substitution Rule for Indefinite Integrals have been prepared according to the Mathematics exam syllabus.
Information about Substitution Rule for Indefinite Integrals covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Substitution Rule for Indefinite Integrals.
Introduction of Substitution Rule for Indefinite Integrals in English is available as part of our Calculus for Mathematics & Substitution Rule for Indefinite Integrals in
Hindi for Calculus course. Download more important topics related with notes, lectures and mock test series for
Mathematics Exam by signing up for free.
Description
Video Lecture & Questions for Substitution Rule for Indefinite Integrals Video Lecture | Calculus - Mathematics - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Calculus.
Information about Substitution Rule for Indefinite Integrals
Here you can find the meaning of Substitution Rule for Indefinite Integrals defined & explained in the simplest way possible.
Besides explaining types of Substitution Rule for Indefinite Integrals theory, EduRev gives you an ample number of questions to practice Substitution Rule for Indefinite Integrals tests,
examples and also practice Mathematics tests.
|
112 videos|65 docs|3 tests
|
|
Explore Courses for Mathematics exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Viva Questions
,Extra Questions
,Free
,Important questions
,Substitution Rule for Indefinite Integrals Video Lecture | Calculus - Mathematics
,Sample Paper
,past year papers
,Semester Notes
,Previous Year Questions with Solutions
,Objective type Questions
,mock tests for examination
,video lectures
,ppt
,shortcuts and tricks
,MCQs
,Summary
,Exam
,study material
,Substitution Rule for Indefinite Integrals Video Lecture | Calculus - Mathematics
,Substitution Rule for Indefinite Integrals Video Lecture | Calculus - Mathematics
,practice quizzes
;
Study Substitution Rule for Indefinite Integrals on the App
Students of Mathematics can study Substitution Rule for Indefinite Integrals alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Substitution Rule for Indefinite Integrals,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Substitution Rule for Indefinite Integrals is prepared as per the latest Mathematics syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup