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

Exercise 1

Determine the value of the integral $\int_0^1 (8x^3-e^{4x})dx$.
$(9-e^4)/4$
$3-e^4$
$(8-e^4)/4$
$7-e^4$
Determine the value of the integral $\int_0^1 (8x^3-e^{4x})dx$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$3-e^4$
Antwoord 2 correct
Fout
Antwoord 3 optie
$(8-e^4)/4$
Antwoord 3 correct
Fout
Antwoord 4 optie
$7-e^4$
Antwoord 4 correct
Fout
Antwoord 1 optie
$(9-e^4)/4$
Antwoord 1 feedback
Correct: $\int_0^1 (8x^3-e^{4x})dx=[2x^4-\frac{1}{4}e^{4x}]_{x=0}^{x=1}=(2-\frac{1}{4}e^4)-(-\frac{1}{4})=2\frac{1}{4}-\frac{1}{4}e^4$, which can be rewritten as $(9-e^4)/4$.

Go on.
Antwoord 2 feedback
Wrong: $e^{4x}$ is not an antiderivative of $e^{4x}$.

See Antidifferentiation.
Antwoord 3 feedback
Wrong: Note that $e^0=1$.

See Exponential functions.
Antwoord 4 feedback
Wrong: You have to find the antiderivative first, before you plug in $x=0$ and $x=1$.

See Integral.