suppose
f: R--->R has a continuous derivative, f(0)=0, and |f'(x)|<=M for x in [0,1]
show that, |integral(f,0,1)|<= half M
show that, if given f(1)=0, then |integral(f,0,1)|<= quarter M
what could you say if |f'(x)|<= Mx?
suppose
f: R--->R has a continuous derivative, f(0)=0, and |f'(x)|<=M for x in [0,1]
show that, |integral(f,0,1)|<= half M
show that, if given f(1)=0, then |integral(f,0,1)|<= quarter M
what could you say if |f'(x)|<= Mx?