Let f be a function such that f' is continuous on [a,b]. show that $\displaystyle \int _a\,^b\!f(t)f'(t)dt $ = $\displaystyle 1/2[f^2(b) - f^2(a)] $
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Originally Posted by wopashui Let f be a function such that f' is continuous on [a,b]. show that $\displaystyle \int _a^{\,b}\!f(t)f'(t)dt $ = $\displaystyle 1/2[f^2(b) - f^2(a)] $ Substitute $\displaystyle u=f(t)$.
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