Exercise 1 | Wiskunde op Tilburg University

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.

Antwoord 2 feedback

Wrong: Note that

$\dfrac{-2}{x^6}$ is not an antiderivative of

$\dfrac{12}{x^5}$ .

See Antidifferentiation.

Antwoord 3 feedback

Wrong: You have to find an antiderivative before you plug in the value

$x=1$ .

See Integral.

Antwoord 4 feedback

Wrong: What happens when

$t \rightarrow \infty$ .

See Improper integral (film).