Physics I / Fundamental theorem of calculus
Practice question · Select all that apply

Which are direct consequences of the Fundamental Theorem of Calculus?

Hints
  1. The theorem is stated for continuous functions, not for all functions.
  2. One claim generalises well beyond what the theorem guarantees.
Show the answer
  • B. Every continuous function on [a,b] has an antiderivative
  • C. Differentiation and integration are inverse operations
  • D. ddx[∫axf(t) dt]=f(x)\frac{d}{dx}\left[\int_a^x f(t)\,dt\right] = f(x) for continuous ff
Why

the first option overstates: not all bounded functions (e.g., Dirichlet function) are Riemann-integrable.

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