I need help finishing an integration problem. (see attachment)

Question

anonymous · Answer

Here is how far I got.

anonymous · Answer

And here is the solution. I did things a little differently starting out but I should still get the same answer. I am not sure how to complete the problem.

zepdrix · Answer

Hmm I'm surprised you're stuck, you've already done the hard part :)

anonymous · Answer

haha, yeah. I can't remember what do do from here though.

zepdrix · Answer

$$\huge -\frac{1}{2}\ln|1+x^2|\; ]_0^{-\sqrt3}$$

So we'll evaluate this at the upper limit, and then subtract from that, the function evaluated at the lower limit.

$$\large \left(-\frac{1}{2}\ln|1+(\color{royalblue}{-\sqrt3})^2|\right)-\left(-\frac{1}{2}\ln|1+(\color{royalblue}{0})^2|\right)$$

anonymous · Answer

ok, but the 1 + -root(3)^2 is like -3.45... and the answer shows it as ln4

zepdrix · Answer

Squaring the $-\sqrt3$ gives us $+3$.
Which in turn gives us ln|4| for that first term right? :o

anonymous · Answer

ah! right, I was putting it into my calculator wrong.

zepdrix · Answer

oh heh :D

anonymous · Answer

It all makes sense now :) Thank you.