Hi. I'm trying to do the integral Leibniz solved when he calculated pi. It goes as follows:
I know the solution to the integral, but I can't solve it.
Can somebody please show me how this integral is solved?
Thanks in advance.
Here's my stab at it:
Complete the square inside the radical:
Thus, the integral becomes
Now apply the trig substitution . We then see that
The limits of integration change as well!
I leave it for you to verify that the integral becomes
Note that
Try to take it from here.
I hope this helps!
--Chris