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

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

1. What is integration by substitution?
Ans. Integration by substitution, also known as u-substitution, is a technique used in calculus to simplify the integration of complicated functions. It involves substituting a variable with a new one so that the integral can be expressed in terms of the new variable, making it easier to evaluate.
2. How does integration by substitution work?
Ans. Integration by substitution works by choosing a suitable substitution that simplifies the integral. The substitution is often chosen such that the derivative of the new variable appears in the integrand, allowing us to rewrite the integral in terms of the new variable. After evaluating the integral with respect to the new variable, the result is then converted back to the original variable.
3. When should I use integration by substitution?
Ans. Integration by substitution is particularly useful when dealing with integrals that involve compositions of functions, such as exponential or trigonometric functions. It is especially effective when the derivative of the substituted variable can be easily identified within the integrand.
4. Can you provide an example of integration by substitution?
Ans. Sure! Let's consider the integral ∫(2x + 1)^2 dx. To simplify this integral, we can use integration by substitution. Let u = 2x + 1, then du/dx = 2, and we can rewrite the integral as ∫u^2 (du/2). Integrating this expression gives u^3/6 + C, where C is the constant of integration. Finally, we substitute back u = 2x + 1 to obtain the final result of (2x + 1)^3/6 + C.
5. Are there any tips for choosing the substitution in integration by substitution?
Ans. When choosing a substitution, it is often helpful to look for parts of the integrand that resemble the derivative of a function. Common choices include trigonometric functions, exponential functions, and rational functions. It can also be beneficial to consider simplifying expressions or canceling terms before applying the substitution, as this may lead to a more straightforward integral.
204 videos|288 docs|139 tests

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