Integration by Parts Flashcards
What is the formula for Integration by Parts?
∫u dv = uv - ∫v du
In the formula ∫u dv = uv - ∫v du, what does ‘u’ represent?
‘u’ is a differentiable function that is chosen to simplify the integral.
In the formula ∫u dv = uv - ∫v du, what does ‘dv’ represent?
‘dv’ is the differential of another function that will be integrated.
True or False: Integration by Parts can be used for any integral.
False
What is the first step in using Integration by Parts?
Choose ‘u’ and ‘dv’ from the integral.
Fill in the blank: The product of the functions ‘u’ and ‘v’ is subtracted from the integral of _____ in Integration by Parts.
v du
Which function should you typically choose for ‘u’ in Integration by Parts?
A function that becomes simpler when differentiated.
What does ‘du’ represent in the Integration by Parts formula?
‘du’ is the derivative of ‘u’ multiplied by dx.
Multiple Choice: Which of the following is a common choice for ‘dv’ when integrating e^x?
e^x dx
True or False: The order of choosing ‘u’ and ‘dv’ does not affect the outcome of the integral.
False
What is the purpose of Integration by Parts?
To transform a difficult integral into a simpler one.
Fill in the blank: The formula for Integration by Parts is derived from the product rule of _____.
differentiation
What should you do if the resulting integral after applying Integration by Parts is still complex?
You may need to apply Integration by Parts again.
Multiple Choice: Which of the following integrals is best suited for Integration by Parts?
∫x e^x dx
What is a common mnemonic to remember the order of choosing ‘u’ and ‘dv’?
LIATE (Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, Exponential)
True or False: Integration by Parts can be performed on definite integrals.
True
When applying Integration by Parts to a definite integral, what must you remember to do?
Evaluate the limits of integration after applying the formula.
Fill in the blank: After integrating ‘dv’, you will have the function _____ in the Integration by Parts formula.
v
What is the result of applying Integration by Parts twice on the integral ∫x^2 e^x dx?
It will simplify the integral until a solvable form is reached.
True or False: The choice of ‘u’ can change the complexity of the integral significantly.
True
What is the integral of sin(x) dx using Integration by Parts?
It requires a suitable choice for ‘u’ and ‘dv’.
Multiple Choice: Which of these pairs would be a good choice for ‘u’ and ‘dv’ in ∫x ln(x) dx?
u = ln(x), dv = x dx
Fill in the blank: The derivative of ‘u’ is denoted as _____ in the Integration by Parts process.
du
What is the integral of x^n e^x dx using Integration by Parts?
It generally involves repeated application of the formula.
