- #1

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## Homework Statement

[tex]\int \frac{\sqrt{196 x^2-144}}{x} dx[/tex]

## Homework Equations

## The Attempt at a Solution

I first rewrote the integral.....

[tex]\int \frac{\sqrt{(14x)^2-12^2}}{x} dx[/tex]

Then I let.......

14x=12sec[tex]\theta[/tex]

thus....

x=6/7sec[tex]\theta[/tex]

dx=6/7sec[tex] \theta tan \theta d \theta[/tex]

My progression of this problem is as follows:

[tex] \int \frac{\sqrt{(144(sec^2 \theta -1)}}{6/7sec \theta} d \theta[/tex]

[tex]12 \int \frac{tan \theta}{6/7sec \theta}(6/7sec \theta tan \theta) d \theta[/tex]

[tex]12 \int tan^2 \theta d \theta[/tex]

[tex]12 \int sec^2 - 1 \theta d \theta[/tex]

[tex]12 tan \theta [/tex]

I am not sure how to finish the problem after that. I am also not sure I did that right since I am very new at this, but I have a feeling everything I did was right.