Integration by parts (HSC SSCE Mathematics Extension 2): Flashcards
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Practise the cards
10 cards from this deck
What is the formula for integration by parts?
What is the formula for integration by parts?
∫u dv = uv - ∫v du
What does LIATE stand for in choosing u?
What does LIATE stand for in choosing u?
Logarithmic, Inverse trig, Algebraic, Trig, Exponential
When is integration by parts typically used?
When is integration by parts typically used?
For integrals with polynomial, exponential, or trig functions.
What is the first step in integration by parts?
What is the first step in integration by parts?
Choose u and dv from the integrand.
What is a good choice for dv in integration by parts?
What is a good choice for dv in integration by parts?
Choose a function that simplifies the integral process.
What is a scenario for repeated integration by parts?
What is a scenario for repeated integration by parts?
When the integral doesn't simplify after one application.
What technique can simplify integrals before parts?
What technique can simplify integrals before parts?
Integration by substitution.
What is a common practice problem for integration?
What is a common practice problem for integration?
Create recurrence relations like ∫x^n e^x dx.
What is crucial for successful integration by parts?
What is crucial for successful integration by parts?
The right choice of u and dv.
What is the result of ∫x e^x dx?
What is the result of ∫x e^x dx?
xe^x - e^x + C