Integrals involving trigonometric substitution (HSC SSCE Mathematics Extension 1): Quizzes
📚Quizzes
Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
Which substitution is best for integrals with a^2 - x^2?
Which substitution is best for integrals with a^2 - x^2?
x = a sin θ
Which substitution simplifies a^2 + x^2 expressions?
Which substitution simplifies a^2 + x^2 expressions?
x = a tan θ
Which substitution is usually used for x^2 - a^2?
Which substitution is usually used for x^2 - a^2?
x = a sec θ
If x = a sin θ, what is √(a^2 - x^2)?
If x = a sin θ, what is √(a^2 - x^2)?
a cos θ
If x = a tan θ, what is √(a^2 + x^2)?
If x = a tan θ, what is √(a^2 + x^2)?
a sec θ
Using x=2 sin θ for √(4−x^2), the integrand becomes:
Using x=2 sin θ for √(4−x^2), the integrand becomes:
4 cos^2 θ
Under x=2 sin θ, limits x=0 to x=2 map to θ = ?
Under x=2 sin θ, limits x=0 to x=2 map to θ = ?
0 to π/2
Which identity is used to integrate cos^2 θ easily?
Which identity is used to integrate cos^2 θ easily?
cos^2 θ=(1+cos2θ)/2
If x = a sec θ, what is √(x^2 − a^2) in trig form?
If x = a sec θ, what is √(x^2 − a^2) in trig form?
a tan θ
Using x=a sin θ, x=a corresponds to which θ?
Using x=a sin θ, x=a corresponds to which θ?
π/2