9.3.4 Choosing Effective Function Decompositions Flashcards Preview

AP Calculus AB > 9.3.4 Choosing Effective Function Decompositions > Flashcards

Flashcards in 9.3.4 Choosing Effective Function Decompositions Deck (6):
1

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.

2

note

- 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
numerator.
- 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.

3

Which of the following is the best choice for au-substitution for the integral∫2x(x^2−4)^6dx?

u = x ^2 − 4

4

Which of these expressions is the best choice for making a u-substitution for the integral∫sin^32xcos2xdx?

u = sin 2x

5

Which of the following expressions creates a working u-substitution that solves the following integral?
∫x^3sinx^2dx

u = x^ 2

6

What is the best choice for a u-substitution for the integral ∫e^cotx csc^2x dx?

u = cot x

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