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Hi,

I just had this idea pop into my head... Can you use a trig sub with a reference triangle who has sides equal to zero? or more like a value close to zero such as dx or da or something?

For example

integral 1/sqrt(9+dx^2) (dx)^2

would have a reference triangle were the hypotenuse is sqrt(9+dx^2)

one of the legs would be 3

the other leg would be dx

you then could express dx/sqrt(9+dx^2) as either csc(theta) or sec(theta) depending on what leg you set 3 be equal to...

integral 1/sqrt(9+dx^2) (dx)^2 = integral csc(theta) dx

I just had this idea pop into my head... Can you use a trig sub with a reference triangle who has sides equal to zero? or more like a value close to zero such as dx or da or something?

For example

integral 1/sqrt(9+dx^2) (dx)^2

would have a reference triangle were the hypotenuse is sqrt(9+dx^2)

one of the legs would be 3

the other leg would be dx

you then could express dx/sqrt(9+dx^2) as either csc(theta) or sec(theta) depending on what leg you set 3 be equal to...

integral 1/sqrt(9+dx^2) (dx)^2 = integral csc(theta) dx

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