Trig Sub Basics
This is the purpose of trigonometric substitution in integration.
What is to simplify integrals involving square roots of quadratic expressions?
Identify the correct trig sub for ∫ dx / √(4 - x²)
What is x = 2sin(θ)?
Evaluate: ∫ dx / √(1 - x²)
What is arcsin(x) + C?
After substituting x = a*sin(θ), what does √(a² - x²) become?
What is a*cos(θ)?
Evaluate: ∫ dx / (x² + 4)^(3/2)
What is x / (4√(x² + 4)) + C
If the integrand has √(a² - x²), this trig function is used for substitution.
What is sin(θ)?
Choose the right trig sub: ∫ dx / √(x² + 9)
What is x = 3tan(θ)?
Evaluate using trig sub: ∫ dx / √(4 + x²)
What is sinh⁻¹(x/2) + C or ln
After substituting x = a*tan(θ), what does dx become?
What is a*sec²(θ)dθ?
Evaluate: ∫ dx / (x√(x² - 9))
What is (1/3)arcsec(
Trig sub is most useful when the integrand contains this type of expression.
What is a square root of a quadratic expression?
Choose the substitution for ∫ dx / √(x² - 1)
What is x = sec(θ)?
Use trig sub to evaluate: ∫ x / √(x² + 9) dx
What is √(x² + 9) + C
What is the integral of sec³(θ)?
What is (1/2)sec(θ)tan(θ) + (1/2)ln
Evaluate: ∫ x³ / √(x² + 1) dx
What is (1/3)(x² - 2)√(x² + 1) + C
True or False: Trig substitution can be used for rational functions.
What is False?
What identity justifies x = a*sin(θ) when integrating √(a² - x²)?
What is sin²(θ) + cos²(θ) = 1?
Solve using trig sub: ∫ dx / (x²√(x² - 4))
What is (1/4) * sec⁻¹(
After integrating, how do you go back from θ to x?
What is using a right triangle based on the trig substitution?
Solve: ∫ x² / √(9 - x²) dx
What is (1/2)x√(9 - x²) + (9/2)arcsin(x/3) + C
Complete the substitution: x = a * tan(θ) implies dx = __.
What is a * sec²(θ) dθ?
Choose the substitution for ∫ x² / √(x² + 16) dx
What is x = 4tan(θ)?
Evaluate: ∫ x² / √(x² + 1) dx
What is (1/2)x√(x² + 1) - (1/2)ln
With x = 3tan(θ), what is tan(θ) in terms of x?
What is x/3?
Evaluate: ∫ √(x² - 16) / x dx
What is √(x² - 16) - 4ln