7.2 Integration by Parts Flashcards
1
Q
What is integration by parts?
A
A method used to integrate the product of two functions by breaking it down into simpler integrals.
2
Q
What are the steps to using integration by parts?
A
- identify u
- find du
- identify dv which is the rest of the equation
- find v which is the integral of dv
- plugin u, du, dv, v into the equation using the integration by parts formula
2
Q
What is the formula for integration by parts?
A
∫udv=uv−∫vdu
3
Q
What is the purpose of integration by parts?
A
To simplify an integral that is a product of two functions, especially when one part becomes simpler after differentiation.
3
Q
What is a common strategy for choosing u?
A
Use the LIATE rule: prioritize u as Logarithmic, Inverse trig, Algebraic, Trigonometric, and Exponential functions in that order
4
Q
How would you apply integration by parts to ∫𝑥𝑒^(𝑥)𝑑𝑥?
A
u=x
du=dx
dv=e^(x)dx
v=e^(x)
then apply the integration by parts formula
