# Chapter 4 - Integration 1 Flashcards

## Mean Values and Volumes of Revolution. This chapter is short and sweet, but be careful not to spiral out of control.

1

Q

What is the mean value of a function?

A

2

Q

What is the formula for the volume of a solid, formed by rotating the curve y = f(x) between x = a/b, a full turn around the x-axis? ]

A

3

Q

What is the formula for the volume of a solid, formed by rotating the curve x = f(y) between y = a/b, a full turn around the y-axis?

A

4

Q

For integrating a circle, what is the expected formula and how is radius treated?

A

To provide proof of a sphere’s volume, you integrate the following expression:

V = π ∫(-r to r) √(r²-x²)dx where r is a constant for radius, and the axis of rotation is the x axis.