2. Calculus II

Applications Of Integration — Quiz

Test your understanding of applications of integration with 5 practice questions.

Practice Questions

Question 1

Which of the following integral applications is used to calculate the total length of a curve?

Question 2

To calculate the volume of a solid of revolution using the shell method, the integral typically involves which of the following components?

Question 3

When finding the center of mass of a system of point masses, the moment about an axis is calculated by summing the product of each mass and its distance from that axis. For a continuous object, this concept extends to integration. Which of the following represents the moment about the x-axis ($ M_x $) for a region bounded by $ y=f(x) $, the x-axis, from $ x=a $ to $ x=b $?

Question 4

A force of $ F(x) = 3x^2 $ Newtons is required to stretch a spring $ x $ meters beyond its natural length. How much work is done in stretching the spring from $ x=1 $ meter to $ x=3 $ meters?

Question 5

To calculate the surface area of a solid of revolution formed by rotating a curve $ x = g(y) $ about the y-axis from $ y=c $ to $ y=d $, which of the following integral formulas is used?