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.

  • 2 worked examples
  • 19 in Integrals

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

1 more worked examplePremium

Evaluate ∫₃¹ 2x dx.

Step-by-step solution locked.

Unlock the full working. CalcRef Premium opens the step-by-step solution above, and 141 worked solutions across the whole library - the intermediate lines, not just the answer. The formula statement, its conditions, its variables and the first worked example stay free on every page.
See PremiumBrowse the free reference

See all 19 Integrals formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.

Common questions

What is the Reversal of Limits?

Switching the limits of integration negates the integral. It is one of the integrals formulas in the CalcRef reference.

How do you use the Reversal of Limits?

Worked example. If ∫₁⁴ f(x) dx = 5, find ∫₄¹ f(x) dx. ∫₄¹ f(x) dx = -∫₁⁴ f(x) dx = -5. Answer: -5.

Practice

Quiz yourself on Integrals

Reversal of Limits is one of 19 Integrals formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.

Take today's free quizAll 19 Integrals formulas