# History Behind Integral Error Between $\pi$ and $22/7$

Looking at an expression for $\pi$

$$\pi = \frac{22}7-\int_0^1 \frac{x^4(1-x)^4}{1+x^2} \ dx$$

it seems to me that the integral expression is the error between the approximation $\frac{22}7$ and $\pi$. Is there any history behind the discovery of this integral? Was it tied to the error between the two numbers or was it discovered separately and only later applied?

• Related (but not the answer to this exact question): math.stackexchange.com/questions/1079024/… I guess someone playing around with integrals of this form stumbled on this relationshihp. – Simon S Mar 11 '15 at 18:25
• I think it was on the 1968 Putnam exam, so it's older than that. Here is a Wikipedia article about this equality. ${}\qquad{}$ – Michael Hardy Mar 11 '15 at 18:25
• @MichaelHardy Thanks for the Wikipedia article but it doesn't really explain where the integral as the exact error came from. – Gabriel Mar 11 '15 at 18:29