Thread: Leibniz' pi integral

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.

Originally Posted by espen180

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