After A1 from the 1968 Putnam:

$$\frac {22}7 - \pi = \int_0^1 \frac{x^4(1-x)^4}{1+x^2}dx \gt 0$$

Integral proofs that $355/113 \gt \pi$.

After A1 from the 1968 Putnam:

$$\frac {22}7 - \pi = \int_0^1 \frac{x^4(1-x)^4}{1+x^2}dx \gt 0$$

Integral proofs that $355/113 \gt \pi$.

I expect that there should be a proof of Jensen's inequality as an integral of a nonnegative quantity.