Trigonometric Substitution

[ivory comet]

This is a trigonometric substitution problem but the thing is I don't know how to solve it. I mean I was only able to solve half of it. The other half I don't know anymore. I need help 😭

[ionic pawn]

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[wicked oasis]

Here are some common substitutions for functions containing square roots of quadratics.

1. √(a^2 - x^2): x = a sin(t).
2. √(a^2 + x^2): x = a tan(t).
3. √(x^2 - a^2): x = a/cos(t).

[ivory comet]

This is the substitution given to us:

a²+x² let x=atanθ dx=asec²θdθ

a²-x² let x =asinθ dx=acos²θdθ

[wet crest]

yup, use one of those

[wicked oasis]

Well, yeah. That's what I said.
Though, you forgot the roots.

[ivory comet]

+close