All Flashcards
What are the differences between u-substitution and Integration by Parts?
u-substitution: Reverses the chain rule, simplifies composite functions. | Integration by Parts: Reverses the product rule, simplifies products of functions.
Explain the purpose of Integration by Parts.
To simplify integrals involving the product of two functions by transforming them into simpler integrals.
How does Integration by Parts relate to the product rule?
It's the reverse process of the product rule for differentiation.
Why is choosing 'u' and 'dv' important?
Proper selection simplifies the integral, making it easier to solve.
What is Integration by Parts?
A technique to integrate the product of two functions, based on the product rule for differentiation.
Define 'u' in Integration by Parts.
A selected part of the integrand that is differentiated.
Define 'dv' in Integration by Parts.
A selected part of the integrand that is integrated.
What is 'du' in Integration by Parts?
The derivative of 'u' with respect to the variable of integration.
What is 'v' in Integration by Parts?
The antiderivative (integral) of 'dv'.