Finding volume of solid

Question

As a hardworking student, plagued by too much homework, you spend all night doing math homework. By 6am, you imagine yourself to be a region bounded by

y=10x^2

x=0

x=1

y=0

As you grow more and more tired, the world begins to spin around you. However, according to Newton, there is no difference between the world spinning around you, and you spinning around the world. Unfortunately, you are so tired that you think the world is the x-axis. What is the volume of the solid you (the region) create by spinning about the x-axis?

Answer 1

For this story, use the disk method formula

V = ∫^b_a π(f(x))²dx

where f(x) = y = 10x², a=0, b = 1

Which is a simple definite integral to solve.