Chapter 4 - Integration 1

Question 1

What is the mean value of a function?

Answer 1

Question 2

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? ]

Answer 2

Question 3

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?

Answer 3

Question 4

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

Answer 4

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.