Question

Find the area of the surface obtained by rotating the curve y=4x^3 from x=0 to x=4 about the x-axis.

Answer 1

kinda like a trumpet shape when we rotate the curve right?

Answer 2

yes

Answer 3

we can take the radius as being 4x^3

Answer 4

use the disk method

Answer 5

\[\int\limits_{0}^{4}\pi[4x^3]^2dx\]

Answer 6

derivative is 12x^2?

Answer 7

\[4\pi \int\limits_{0}^{4}x^3dx\]

Answer 8

find the anti derivative of x^3

Answer 9

x^4/4?

Answer 10

yup, which means you got to do:

\[\pi x^4\] evaluated from 0 to 4

Answer 11

that gives me 256pi

Answer 12

nice job

Answer 13

thank you

Answer 14

oh this one also needs the surface area, how come you didnt stop me?

Answer 15

i just realized it.