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Integration by Parts - Integrals Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Integration by Parts - Integrals Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is integration by parts?
Ans. Integration by parts is a technique used in calculus to evaluate integrals of the product of two functions. It is based on the product rule for differentiation, where the derivative of the product of two functions can be expressed in terms of the derivatives of the individual functions.
2. How does integration by parts work?
Ans. Integration by parts involves choosing two functions, typically denoted as u and v, and applying the formula: ∫u dv = uv - ∫v du Here, u is chosen such that its derivative is simpler than the original integrand, while dv is chosen such that its integral is easier to evaluate. The goal is to simplify the integral by rearranging the terms on the right side of the equation.
3. When should I use integration by parts?
Ans. Integration by parts is useful when the integral of a product of two functions cannot be easily evaluated by other methods such as substitution or simplification. It is particularly helpful when one of the functions has a simple derivative, while the other has a simple integral.
4. What is the formula for integration by parts?
Ans. The formula for integration by parts is given by: ∫u dv = uv - ∫v du In this formula, u and v are the chosen functions, and du and dv represent their respective differentials.
5. Can integration by parts be applied multiple times?
Ans. Yes, integration by parts can be applied multiple times if necessary. This technique can be used iteratively to simplify complex integrals by repeatedly choosing new u and v functions. However, care must be taken to avoid falling into an infinite loop or creating a more complicated integral.
204 videos|288 docs|139 tests

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