Determine the value of the integral $\int_1^{\infty} \dfrac{12}{x^5} dx$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$2$
Antwoord 2 correct
Fout
Antwoord 3 optie
$12$
Antwoord 3 correct
Fout
Antwoord 4 optie
$\infty$
Antwoord 4 correct
Fout
Antwoord 1 optie
$3$
Antwoord 1 feedback
Correct: $\int_1^t \dfrac{12}{x^5} dx=[\dfrac{-3}{x^4}]_{x=1}^{x=t}=\dfrac{-3}{t^4}+3$. If $t \rightarrow \infty$, then $\dfrac{-3}{t^4}+3\rightarrow 0+3=3$.
Go on.
Go on.
Antwoord 2 feedback
Wrong: Note that $\dfrac{-2}{x^6}$ is not an antiderivative of $\dfrac{12}{x^5}$.
See Antidifferentiation.
See Antidifferentiation.
Antwoord 3 feedback
Antwoord 4 feedback