Physics I / Integrals as accumulation
Practice question · Select all that apply

Which are valid properties of the definite integral?

Hints
  1. Integration is linear: it respects sums and constant multiples.
  2. Ask whether any listed property would also survive for a product.
Show the answer
  • A. ∫abfdx\int_a^b f dx = −∫bafdx\int_b^a f dx
  • C. ∫ab(f+g)dx\int_a^b (f + g) dx = ∫abfdx\int_a^b f dx + ∫abgdx\int_a^b g dx
  • D. ∫abc⋅fdx\int_a^b c\cdot f dx = c·∫abfdx\int_a^b f dx
Why

the second option is false: the integral of a product is not the product of integrals.

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