How Can I Solve This Improper Integral With Absolute Value?

[dan]

Hi there
I'm having trouble solving this integral!

Evaluate the improper integral
int[1/(sqrt{absolute value(1-4x^2)})]dx where the upper limit=1, lower limit=0

without ignoring the absolute value sign?


Thank you in advance

 

[HallsofIvy]

What exactly do you mean by "without ignoring the absolute value"?
Since this has an absolute value, one CAN'T do while ignoring the absolute value!

The obvious way to integrate this is to separate into two integrals, one from 0 to 1/2 and the other from 1/2 to 1:
integral (x=0 to 1/2) (1/sqrt(1- 4x^2))dx+ integral(x= 1/2 to 1)(1/sqrt(4x^2- 1))dx and then use trigonometric substitutions.

Using the definition of absolute value is certainly NOT ignoring it!