Podcast
Play an AI-generated podcast conversation about this lesson
Questions and Answers
When finding the surface area of revolution, what does the term √(1 + (f'(x))^2) represent?
When finding the surface area of revolution, what does the term √(1 + (f'(x))^2) represent?
- The element of surface area
- The circumference of the curve
- The radius of revolution
- The element of arc length (correct)
What is the formula for finding the surface area of revolution when rotating the curve y = f(x) about the x-axis?
What is the formula for finding the surface area of revolution when rotating the curve y = f(x) about the x-axis?
- π∫[a,b] (f(x))^2 (1 + (f'(x))^2) dx
- 2π∫[a,b] f(x) √(1 + (f'(x))^2) dx (correct)
- π∫[a,b] (f(x))^2 √(1 + (f'(x))^2) dx
- 2π∫[a,b] f(x) (1 + (f'(x))^2) dx
What is the formula for finding the volume of revolution when rotating the curve y = f(x) about the x-axis?
What is the formula for finding the volume of revolution when rotating the curve y = f(x) about the x-axis?
- π∫[a,b] (f(x))^3 dx
- π∫[a,b] f(x) √(1 + (f'(x))^2) dx
- π∫[a,b] (f(x))^2 dx (correct)
- π∫[a,b] f(x) dx
