Practice question · Select all that apply
Select every statement that follows from the Fundamental Theorem of Calculus.
Hints
- Four options are direct consequences of the two parts; one is a claim about what formulas exist.
- Recall why the lesson mentions that computers still evaluate some integrals numerically.
Show the answer
- A. Accumulation and rate of change are inverse operations
- B. The choice of antiderivative does not affect the answer
- C. A definite integral can be computed without any summation
- E. Reversing the limits of integration flips the sign of the answer
Why
The theorem makes evaluation a subtraction, makes the constant irrelevant, and forces F(a) - F(b) to be the negative of F(b) - F(a). It says nothing about whether a formula for the antiderivative exists, many do not, which is exactly why numerical methods survive.
Practise The Fundamental Theorem of Calculus
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