Surface Area of Revolution about x axis

[mikbear]

Homework Statement

x^2 + (y - 2)^2 = 1
The hint given by the question was to split the function into 2

Homework Equations

Surface Area about x axis

The Attempt at a Solution

So i did this.
(y - 2)^2 = 1 - x^2
y = √(1 - x^2) +2 and y = 2 - √(1 - x^2)

The range I calculated
when y= 0; x = - √(-3) and x = √(-3)

I use the formula ∫ 2∏ * (√(1-x^2) + 2)√(1 + x^2/(1 - x^2))dx

Then i got stuck as it became messy

 

[mfb]

when y= 0; x = - √(-3) and x = √(-3)

That just means that y=0 does not happen. Your integration limits are determined by something else...

I use the formula ∫ 2∏ * (√(1-x^2) + 2)√(1 + x^2/(1 - x^2))dx

How did you get that formula?

 

[LCKurtz]

Homework Statement

x^2 + (y - 2)^2 = 1
The hint given by the question was to split the function into 2

Homework Equations

Surface Area about x axis

The Attempt at a Solution

So i did this.
(y - 2)^2 = 1 - x^2
y = √(1 - x^2) +2 and y = 2 - √(1 - x^2)

The range I calculated
when y= 0; x = - √(-3) and x = √(-3)

I use the formula ∫ 2∏ * (√(1-x^2) + 2)√(1 + x^2/(1 - x^2))dx

Then i got stuck as it became messy

The first step would be to identify the curve that is being rotated. Have you drawn its graph? Do you see why you would want to use the hint?