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Why can Maple yield the result of int(q(t)*diff(q(t),t),t) = (q(t)^2)/2 (indefinite integral) but with int(q(t)*diff(q(t),t),t=0..t) (definite integral) it returns unevaluated?

I expect the result of the definite integral to be (q(t)^2 - q(0)^2)/2.

brunoleos
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1 Answers1

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int(q(t)*diff(q(t),t),t=0..t,continuous);

                    2           2
           -1/2 q(0)  + 1/2 q(t)
acer
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  • @sonEtLumiere The fundamental theorem of calculus only applies to continuous functions. It's not known a priori whether q is continuous. – Carl Love Aug 21 '20 at 08:10
  • The result you're expecting is not correct in general. The `continuous` option to the `int` command allows you to aver that the integrand is continuous and force the issue. – acer Aug 21 '20 at 17:42