- #1
Slimsta
- 190
- 0
Homework Statement
[tex]$\int \frac{\sqrt{1-4x^2}dx}{x}$[/tex]
Homework Equations
The Attempt at a Solution
im stuck and i have no idea why I am getting the wrong answer.
let 2x = sin[tex]\phi[/tex]
dx = cos[tex]\phi[/tex] d[tex]\phi[/tex] / 2
[tex]$\int \frac{\sqrt{1-(2x)^2}dx}{x}$[/tex]=[tex]$\int \frac{\sqrt{1-(sin\phi)^2}dx}{x}$[/tex]=[tex]$\int \frac{\sqrt{cos\phi^2}dx}{x}$[/tex]=[tex]$\int \frac{cos\phi dx}{x}$[/tex]=
[tex]$\int \frac{cos\phi^2 d\phi}{2x}$[/tex]= [tex]$ .5\int \frac{cos\phi^2 d\phi}{x}$ =[/tex] [tex]$ .5\int \frac{.5(1+cos(2\phi)) d\phi}{x}$= [/tex]
[tex]$ (1/4) \int 1/x+cos(2\phi)/x d\phi $[/tex]
am i even on the right truck?