2. Pure Calculus

Applications Integrals — Quiz

Test your understanding of applications integrals with 5 practice questions.

Practice Questions

Question 1

A region is bounded by the curve $y = x^2 + 2$, the x-axis, and the lines $x=0$ and $x=2$. Which of the following integrals represents the area of this region?

Question 2

A solid is generated by rotating the region bounded by $y = x^2$, the x-axis, and $x=2$ around the x-axis. Which integral setup correctly represents the volume of this solid of revolution using the disk method?

Question 3

A variable force $F(x) = (4x + 3)$ Newtons acts on an object. How much work is done (in Joules) in moving the object from $x=1$ m to $x=3$ m?

Question 4

If the rate of water flowing into a tank is given by $R(t) = 6t$ liters per minute, where $t$ is in minutes, how much water accumulates in the tank during the first 4 minutes?

Question 5

When finding the area between two curves, $y = f(x)$ and $y = g(x)$, where $f(x) = x+2$ and $g(x) = x^2$, over the interval $[0, 1]$, which integral setup is correct?