4. Integration

Integration Basics — Quiz

Test your understanding of integration basics with 5 practice questions.

Practice Questions

Question 1

Given that the derivative of a function $F(x)$ is $f(x) = (3x - 2)^2$, what is the antiderivative $F(x)$?

Question 2

If the velocity of a particle is given by $v(t) = 4t^3 - 6t^2 + 2t - 1$ meters per second, and its initial position at $t=0$ is $s(0) = 5$ meters, what is the position function $s(t)$?

Question 3

The marginal revenue for a company is given by $MR(x) = 200 - 0.4x$, where $x$ is the number of units sold. If the total revenue from selling 0 units is $0$, what is the total revenue function $R(x)$?

Question 4

If the acceleration of an object is given by $a(t) = 12t^2 - 6t + 2$ meters per second squared, and its initial velocity is $v(0) = 4$ m/s, what is the velocity function $v(t)$?

Question 5

The gradient of a curve is given by $\frac{dy}{dx} = 6x^2 - 8x + 3$. If the curve passes through the point $(1, 2)$, what is the equation of the curve, $y$?