Practice question · Multiple choice
The Fundamental Theorem lets you evaluate an integral by finding any antiderivative. Why does any one work, when there are infinitely many?
Hints
- Take F(x) and F(x) + 7. Compute both differences at b and a.
- Ask what survives a subtraction of two functions that differ by a constant.
Show the answer
D. Because they differ only by a constant, which cancels in F(b) − F(a)
Why
The +7 appears at both ends and subtracts away, so every antiderivative gives the same difference. That is what makes the theorem usable, you may take the laziest antiderivative you can find, and the ambiguity that makes indefinite integration a family is exactly the part the definite integral discards.
Practise The Fundamental Theorem of Calculus
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