This proof uses integral calculus. If 22/7 > π, then 22/7 - π is a positive number. We claim that this integral comes out to 22/7 - π.
That the integral is positive follows from the fact that the integrand is a quotient whose numerator and denominator are both nonnegative, being sums or products of even powers of real numbers. So the integral from 0 to 1 is positive. It remains to be shown that this integral evaluates to 22/7 - π. To wit:
(expanded terms in numerator) (performed w:polynomial long division, an important aspect of formulating w:algebraic geometry) (definite integration) (substitute one for x, then zero for x, and subtract them—arctan(1) = π/4) (addition)
Thus, 22/7 - π > 0 and it follows that 22/7 > π