Practice question · Multiple choice
Indefinite integrals always carry '+ C'. Why is dropping it a real error rather than untidiness?
Hints
- Differentiate x², x² + 5 and x² − 100. Compare the results.
- Ask what information differentiation threw away, and who has to put it back.
Show the answer
B. Because differentiation destroys constants, so the family shares one
Why
Every vertical shift has the same slope everywhere, so differentiation loses the constant and no antiderivative can recover it. The C is the honest record of that loss, and in a differential equation it is where the initial condition goes, which is why setting it to zero silently assumes the system started at the origin.
Practise Antiderivatives and Indefinite Integrals
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