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.
