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Status: Tags: #math/calculus/integrals Links: Integral Calculus Notes

Trigonometric Substitution

Used mostly for quadratics inside square roots

Notes

Types of Substitution

• Where $a>0$ and $x$ is a variable

Steps

1. Turn x and dx into appropriate substitutions
2. Turn contents of square root into appropriate identities
3. Factor out the a value
4. Turn contents into identity again and apply square root
5. Integrate remaining contents (split or use identities if necessary)
6. Map out triangle in QI (find missing value using Pythagorean Theorem)
7. Substitue values of $θ$ into x equivalents

Mistakes

• Section J part II
  • Set denominator as sec^2x instead of secx
    • Maybe I thought x = ^ ?

Anki

START Cloze {1:$\sqrt{a^2-x^2}$::Expression} uses {2:$x = a\sin θ$::Substitution} and {3:$1-\sin^2 θ = \cos^2$ ::Identity} Back: DECK: IntegralCalculus Tags: Calculus

END

START Cloze {$\sqrt{x^2-a^2}$::Expression} uses {$x = a\sec θ$::Substitution} and {$\sec^2 θ - 1 = \tan^2 θ$ ::Identity} Back: DECK: IntegralCalculus Tags: Calculus

END

START Cloze {$\sqrt{a^2+x^2}$::Expression} uses {$x = a\tan θ$::Substitution} and {$\tan^2 θ + 1 = \sec^2 θ$::Identity} Back: DECK: IntegralCalculus Tags: Calculus

END

START Cloze Trigonometric Substitution: {Turn x and dx into appropriate substitutions::Step 1} {Turn contents of square root into appropriate identities::Step 2} {Factor out the a value::Step 3} {Turn contents into identity again and apply square root::Step 4} {Integrate remaining contents (split or use identities if necessary)::Step 5} {Map out triangle in QI (find missing value using Pythagorean Theorem)::Step 6} {Substitue values of $θ$ into x equivalents::Step 7} Back: DECK: IntegralCalculus Tags: Calculus

END

Practice

Section J

References:

Created:: 2021-06-12 15:03