Dimostrazione che 22/7 è maggiore di π: differenze tra le versioni

:<math>\pi \approx 3.141592\dots\,</math>

 

 

 

:<math>0<\int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx=\frac{22}{7}-\pi.</math>

 

 

 

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.