![]() ![]() Or take the easiest option and ask Mathematica to try to prove they are equal:Īnother calculus-related question concerns differentiation followed by indefinite integration. In this case, you can try simplifying the integrand as well as the result: Here, the simplified result is different from the integrand: That won’t necessarily work if you didn’t give the original integrand in its simplest form: You can often discover this fact by using Simplify or FullSimplify: However, this result is mathematically equivalent to the integrand sin( x 3). In complicated cases, it can appear that Mathematica is not giving back the original function: (Note that sin( x) is equivalent to sin( t) up to renaming of the variable x or t.) This is a consequence of the fundamental theorem of calculus. The derivative of a definite integral with respect to its upper bound (with a constant lower bound) is equal to the integrand: Read below or watch this screencast for the answer (we recommend viewing it in full-screen mode): Why doesn’t differentiating after integrating always return the original function? This week’s question comes from Kutha, a math lecturer: ![]() You can submit your question directly to the Q&A Team. Got questions about Mathematica? The Wolfram Blog has answers! We’ll regularly answer selected questions from users around the web. ![]()
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