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  3. Chapter 6: Areas and integrals
  4. Antidifferentiation
  5. Exercise 3

Exercise 3

Determine the value of the integral $\int_1^4 (2x\sqrt{x})dx$.
$24\frac{4}{5}$
$30$
$14$
$31$
Determine the value of the integral $\int_1^4 (2x\sqrt{x})dx$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$30$
Antwoord 2 correct
Fout
Antwoord 3 optie
$14$
Antwoord 3 correct
Fout
Antwoord 4 optie
$31$
Antwoord 4 correct
Fout
Antwoord 1 optie
$24\frac{4}{5}$
Antwoord 1 feedback
Correct: $\int_1^4 (2x\sqrt{x})dx=[\frac{4}{5}x^\frac{5}{2}]_{x=1}^{x=4}=[\frac{4}{5}x^2\sqrt{x}]_{x=1}^{x=4}=\frac{128}{5}-\frac{4}{5}=\frac{124}{5}=24\frac{4}{5}$.

Go on.
Antwoord 2 feedback
Wrong: $2x^2$ is not an antiderivative of $2x\sqrt{x}$.

See Antidifferentiation.
Antwoord 3 feedback
Wrong: You first have to find an antiderivative, before you plug in $x=1$ and $x=4$.

See Integral.
Antwoord 4 feedback
Wrong: Do not forget the term $2$.

See Integral.