trig_substitution

trig_substitution - Sec0on8.3 Integralsinvolving 2 x 2 a a...

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Trigonometric Subs0tu0on Sec0on 8.3
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a 2 x 2 = a cos( θ ) Subs0tu0on: Back‐subs0tu0on: = sin 1 ( x / a ) sin( ) = x a cos( ) = a 2 x 2 a x = a sin( ) dx = a cos( ) d a 2 x 2 = a cos( ) Integrals involving a 2 x 2 x = a sin( ) a a x
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a 2 + x 2 Subs0tu0on: Back‐subs0tu0on: θ = tan 1 ( x / a ) sin( ) = x a 2 + x 2 cos( ) = a a 2 + x 2 x = a tan( ) dx = a sec 2 ( ) d a 2 + x 2 = a sec( ) Integrals involving a 2 + x 2 a = a 2 + x 2 cos( ) x = a tan( ) a x
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Subs0tu0on: Back‐subs0tu0on: θ = sec 1 ( x / a ) sec( ) = x a sin( ) = x 2 a 2 x , cos( ) = a x tan( ) = x 2 a
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trig_substitution - Sec0on8.3 Integralsinvolving 2 x 2 a a...

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