4. Integrals

Antiderivatives — Quiz

Test your understanding of antiderivatives with 5 practice questions.

Practice Questions

Question 1

If the acceleration of a particle is given by $a(t) = 6t - 2$ and its initial velocity is $v(0) = 3$, what is the velocity function $v(t)$?

Question 2

Given that the rate of change of a function is $f'(x) = 4x^3 - 3x^2 + 2x - 1$ and $f(1) = 5$, determine the specific function $f(x)$?

Question 3

If the marginal revenue of a product is given by $MR(x) = 30 - 0.06x$, where $x$ is the number of units sold, find the total revenue function $R(x)$ assuming $R(0) = 0$?

Question 4

Which of the following is the antiderivative of $f(x) = \frac{1}{\sqrt[4]{x}}$?

Question 5

If the velocity of an object is given by $v(t) = \sin(t) - \cos(t)$ and its initial position is $s(0) = 5$, what is the position function $s(t)$?