Flashcards in 9.3.4 Choosing Effective Function Decompositions Deck (6):
Choosing Effective Function Decompositions
• Experiment with different choices for u when using integration by substitution. A good choice is one whose derivative is expressed elsewhere in the integrand.
• When working with integrands that include trigonometric expressions, it is sometimes necessary to rewrite those expressions using trig identities.
- When applying integration by substitution to composite
functions, there may be several choices for u.
- In the case of a rational function, the best choice is often the denominator.
- In this example, du/2 produces the expression in the
- You may want to express trigonometric integrands in terms of sine and cosine before integrating.
- Since the denominator has cosx raised to a power, choose u to be cosx. Then –du produces the expression in the numerator.
Which of the following is the best choice for au-substitution for the integral∫2x(x^2−4)^6dx?
u = x ^2 − 4
Which of these expressions is the best choice for making a u-substitution for the integral∫sin^32xcos2xdx?
u = sin 2x
Which of the following expressions creates a working u-substitution that solves the following integral?
u = x^ 2