Exercise · ZW-ANTIDERIVATIVE-001 · ★★☆ Intermediate
If \(F\) and \(G\) are antiderivatives of the same function on an interval, then...
Choose one option.
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- A. F − G is constant
Explanation
If F' = G' = f, then (F − G)' = 0, so F − G is constant on the interval. That is why the indefinite integral carries "+ C".
Review the concept: Antiderivative
An antiderivative of \(f\) is a function \(F\) such that \(F^{\prime}=f\). If \(F\) is an antiderivative of \(f\), all the others on an interval differ from \(F\) by a constant.
\[F'(x)=f(x)\]
More practice problems: antiderivative
- ZW-ANTIDERIVATIVE-002 Which is an antiderivative of f(x)=cos x?
- ZW-ANTIDERIVATIVE-003 Which is an antiderivative of f(x)=(1)/(x)?
- ZW-ANTIDERIVATIVE-004 Which is an antiderivative of f(x)=sec^2 x?
- ZW-ANTIDERIVATIVE-005 Which is an antiderivative of f(x)=x^2?
- ZW-ANTIDERIVATIVE-006 Which is an antiderivative of f(x)=e^x?
- ZW-ANTIDERIVATIVE-007 Which is an antiderivative of f(x)=sin (2x )?
- ZW-ANTIDERIVATIVE-008 Let f(x)=0 on D=(-1,0)∪(0,1). Which statement is true?
- ZW-ANTIDERIVATIVE-009 Which is an antiderivative of f(x)=(1)/(x^2)?