Determine the value of the integral $\int_{-1}^\infty 3\sqrt{x+1} dx$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$0$
Antwoord 2 correct
Fout
Antwoord 3 optie
$-1$
Antwoord 3 correct
Fout
Antwoord 4 optie
$-\infty$
Antwoord 4 correct
Fout
Antwoord 1 optie
$\infty$
Antwoord 1 feedback
Correct: $\int_{-1}^t 3\sqrt{x+1} dx=[\frac{1}{2}(x+1)^\frac{3}{2}]_{x=-1}^{x=t}=\frac{1}{2}(t+1)\sqrt{t+1}-0$. If $t\rightarrow \infty$, then $\frac{1}{2}(t+1)\sqrt{t+1}\rightarrow \infty$. We say that the integral is undetermined.
Go on.
Go on.
Antwoord 2 feedback
Wrong: Note that $\dfrac{3}{\sqrt{x+1}}$ is not an antiderivative of $3\sqrt{x+1}$.
SeeAntidifferentiation.
SeeAntidifferentiation.
Antwoord 3 feedback
Antwoord 4 feedback