- #1
Nano-Passion
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I wanted to try an alternative method to the proverbial technique used in trig substitution. Is this method a dead-end or is there hope for it?
[tex] \int \frac{\sqrt{x^2-3}}{x} dx[/tex]
Using trig substitution
[tex]c^2=a^2+b^2[/tex]
[tex]a = \sqrt{c^2-b^2}[/tex]
[tex]∴ c = x, b = \sqrt{3}[/tex]
Assigning these values to a triangle, where a is adjacent to theta and b is opposite to theta we get..
[tex] \int \frac{\sqrt{x^2-3}}{x} dx = \int \frac{a}{x} dx = \int cos \theta dx[/tex]
And I've hit a wall. I can't seem to be able to adequately convert dx to dθ.
[tex] \int \frac{\sqrt{x^2-3}}{x} dx[/tex]
Using trig substitution
[tex]c^2=a^2+b^2[/tex]
[tex]a = \sqrt{c^2-b^2}[/tex]
[tex]∴ c = x, b = \sqrt{3}[/tex]
Assigning these values to a triangle, where a is adjacent to theta and b is opposite to theta we get..
[tex] \int \frac{\sqrt{x^2-3}}{x} dx = \int \frac{a}{x} dx = \int cos \theta dx[/tex]
And I've hit a wall. I can't seem to be able to adequately convert dx to dθ.