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  3. Chapter 6: Areas and integrals
  4. Integral
  5. Exercise 1

Exercise 1

Determine which of the following functions is an antiderivative of $f(x)=e^{2x}+\frac{1}{\sqrt{x}}$.
$F(x)=\frac{1}{2}e^{2x}+2\sqrt{x}-10$
$F(x)=e^{2x}+\frac{1}{x\sqrt{x}}+3$
$F(x)=\frac{1}{2}e^{2x}+\sqrt{x}$
$F(x)=e^{2x}+2\sqrt{x}-x$
Determine which of the following functions is an antiderivative of $f(x)=e^{2x}+\frac{1}{\sqrt{x}}$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$F(x)=e^{2x}+\frac{1}{x\sqrt{x}}+3$
Antwoord 2 correct
Fout
Antwoord 3 optie
$F(x)=\frac{1}{2}e^{2x}+\sqrt{x}$
Antwoord 3 correct
Fout
Antwoord 4 optie
$F(x)=e^{2x}+2\sqrt{x}-x$
Antwoord 4 correct
Fout
Antwoord 1 optie
$F(x)=\frac{1}{2}e^{2x}+2\sqrt{x}-10$
Antwoord 1 feedback
Correct. $F(x)$ is an antiderivative of $f(x)$, because $F(x)'=f(x)$.

Go on.
Antwoord 2 feedback
Wrong. Note that $(e^{2x})'\not=e^{2x}$.

See Chain rule.
Antwoord 3 feedback
Wrong. Note that $(\sqrt{x})'\not=\frac{1}{\sqrt{x}}$.

See Derivatives of elementary functions.
Antwoord 4 feedback
Wrong. Pay attention to the final term $-x$.

Try again.