Question

Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis.

We have to use the surface area formula of revolution.


Integral (2pi*f(x)sqrt(1+f'(x)^2))dx

Answer 1

INT(2PI*4x*sqrt(1+4^2))dx from x=0 to 1
2PI*2x^2*sqrt(17) from x=0 to x=1

2PI (2*sqrt(17)

comparing this to the cone formula.
area= PI (4)(1+sqrt17)

What is the difference? Your formula did not count the area at x=1 (the bottom of the cone as surface area).

Answer 2

why don't you go from 4 to 0 if its around the y-axis?

Answer 3

You can do that too.