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?
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Originally Posted by szpengchao 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? Integrating: whenever By the FTC: Thus: Integrating again: Therefore: Since we get the desired result All the other parts are similar, try to do them and then ask if you still have doubts. 1
Originally Posted by PaulRS Integrating: whenever By the FTC: Thus: Integrating again: Therefore: Since we get the desired result All the other parts are similar, try to do them and then ask if you still have doubts. 1 how can u get the second ques?
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