Mathematics I / The Fundamental Theorem of Calculus
Practice question · True or false

The Fundamental Theorem shows that differentiation and integration are inverse operations.

Hints
  1. What does differentiating an area function give back?
  2. F(x)=axfF(x) = \int_a^x f, then F=fF' = f.
Show the answer

True

Why

True. Part 1 says differentiating the accumulated-area function returns the integrand; Part 2 says a definite integral can be evaluated by any antiderivative. Linking area to slope, two apparently unrelated ideas, is what turned integration from a limit computation into an algebraic one.

Read the lesson: The Fundamental Theorem of Calculus →

Practise The Fundamental Theorem of Calculus

The app has 7 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.

More questions on The Fundamental Theorem of Calculus