Exercise 2 | Wiskunde op Tilburg University

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.

Antwoord 2 feedback

Wrong: Note that

$\dfrac{3}{\sqrt{x+1}}$ is not an antiderivative of

$3\sqrt{x+1}$ .

SeeAntidifferentiation.

Antwoord 3 feedback

Wrong: Reconsider the concept of an antiderivative.

See Antiderivative.

Antwoord 4 feedback

Wrong: Note that

$3\sqrt{x+1}$ is a non-negative function.

See Area and integral.