
Which is correct ?
Hi.
(Let, Int=integral and Sqrt=square root and In=natural log)
In a math book I found that
Int( Sqrt(Z^2A^2) )
= (A^2)/2 * ( (Z*Sqrt(Z^2A^2))/(A^2)  In((Z+sqrt(z^2A^2))/A) )
= (Z*Sqrt(Z^2A^2))/2  ( (A^2)/2 * In((Z+sqrt(z^2A^2))/A) )
but with my TI89 titanium calculator the same integral gave
Int( Sqrt(Z^2A^2) )
= (Z*Sqrt(Z^2A^2))/2  ( (A^2)/2 * In(Z+sqrt(z^2A^2)) )
After some working out on paper, I found my calculator gave the wrong result. I not too sure why this is. Can anyone tell me which is correct ?
Thanks

Which variable is this respect to?
$\displaystyle \int \sqrt{z^2a^2}da$ is much different from $\displaystyle \int \sqrt{z^2a^2}dz$
Jameson

You can check an alleged indefinite integral (antiderivative) by differentiating ...

ah... sorry, it's with repect to z.
thanks

$\displaystyle \int \sqrt{x^2a^2}dx=\frac{x\sqrt{x^2a^2}}{2}\frac{a^2\ln(x+\sqrt{x^2a^2})}{2}$