23/02/19 23:27:45.23 /imHv0Hl0.net
curve(sin,0,10,asp=1)
abline(a=0,b=0.4/pi)
curve(sin(x)-cos(x)*x,0,10)
abline(h=0,lty=3)
x0=uniroot(\(x) sin(x)-cos(x)*x,c(6,8))$root ; x0
sin(x0)
p=sin(x0)/x0 ; p
# sin(x0)=cos(x0)*x0
# sin(1/p)=cos(1/p)/p
curve(sin,0,10,asp=1)
text(x0,sin(x0),'x0')
segments(0,0,x0,sin(x0))
x1=uniroot(\(x) sin(x)-p*x, c(2,4))$root
text(x1,sin(x1),'x1')
integrate(\(x) sin(x)-p*x,0,x1)$value + integrate(\(x) p*x-sin(x),x1,x0)$value