CalcRef

Integrals · Integral Properties

Reversal of Limits

∫abf(x) dx=−∫baf(x) dx\int_a^b f(x)\, dx = -\int_b^a f(x)\, dx

Switching the limits of integration negates the integral.

Worked examples

If ∫₁⁴ f(x) dx = 5, find ∫₄¹ f(x) dx.
  1. ∫₄¹ f(x) dx = -∫₁⁴ f(x) dx = -5

Answer: -5

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