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More Examples : Integration by Substitution Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on More Examples : Integration by Substitution Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is integration by substitution?
Ans. Integration by substitution, also known as the method of u-substitution, is a technique used in calculus to simplify complex integrals. It involves substituting a new variable, usually denoted as u, in order to transform the integral into a simpler form.
2. How does integration by substitution work?
Ans. Integration by substitution works by choosing an appropriate substitution that simplifies the integral. The chosen substitution involves replacing part of the integrand with a new variable, u, in such a way that the remaining integral becomes easier to solve. After the substitution, the integral is evaluated with respect to the new variable, and then converted back to the original variable.
3. What are the steps involved in integration by substitution?
Ans. The steps involved in integration by substitution are as follows: 1. Identify a suitable substitution by selecting a part of the integrand that can be replaced by a new variable. 2. Calculate the derivative of the new variable with respect to the original variable. 3. Rewrite the integral using the new variable and its derivative. 4. Simplify the integrand by substituting the derivative and the new variable. 5. Evaluate the integral with respect to the new variable. 6. Convert the result back to the original variable if necessary.
4. When should I use integration by substitution?
Ans. Integration by substitution should be used when the integral involves a composition of functions or a complicated expression that can be simplified through substitution. It is particularly useful when the integrand contains a product, quotient, or chain rule, as substitution can help to simplify these types of expressions.
5. Are there any limitations or special cases to consider when using integration by substitution?
Ans. Yes, there are a few limitations and special cases to consider when using integration by substitution. These include: - Choosing an appropriate substitution that simplifies the integral. - Being mindful of the bounds of integration, especially when the substitution changes the limits. - Dealing with multiple substitutions or nested substitutions, which may require a different approach. - Handling cases where the integral cannot be expressed in terms of elementary functions, such as when the integrand is non-algebraic.
204 videos|288 docs|139 tests

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