Finding the Surface Area of Revolution and Arc Length

**miserablestudent** · October 28th 2010, 07:23 PM

a.) Calculate the arc length of y=x^2 from [0,1]

- For this one I used the formula the for arc length and got stuck once I used trig substitution.

b.) Compute the surface area of revolution about the x-axis for y=x^2 from [0,4]

- For this problem I used the formula surface area of revolution, but when I plugged my results in my calculator I got -6,036, which I'm assuming is incorrect.

**skeeter** · October 28th 2010, 07:57 PM

Originally Posted by miserablestudent

a.) Calculate the arc length of y=x^2 from [0,1]

- For this one I used the formula the for arc length and got stuck once I used trig substitution.

b.) Compute the surface area of revolution about the x-axis for y=x^2 from [0,4]

- For this problem I used the formula surface area of revolution, but when I plugged my results in my calculator I got -6,036, which I'm assuming is incorrect.

$\displaystyle \int_0^1 \sqrt{1+4x^2} \, dx$

$\displaystyle x = \frac{\tan{t}}{2}$

$\displaystyle dx = \frac{\sec^2{t}}{2} \, dt$

$\displaystyle \frac{1}{2} \int_0^{\arctan(2)} \sec^3{t} \, dt$

use integration by parts ... $u = \sec{t}$ , $dv = \sec^2{t} \, dt$

note that you'll get $\displaystyle \int \sec^3{t} \, dt = \frac{1}{2}\left[\sec{t}\tan{t} + \int \sec{t} \, dt\right]$

surface area problem ...

$\displaystyle A = 2\pi \int_0^4 x^2 \sqrt{1 + 4x^2} \, dx \approx 817$

**miserablestudent** · October 28th 2010, 08:03 PM

I was able to get the same answer for the second one, but I wasn't able to find the correct anti-derivative.

**skeeter** · October 29th 2010, 05:31 AM

here's what wolfram alpha shows ...

integral of x^2*sqrt(1+4x^2) - Wolfram|Alpha

Thread: Finding the Surface Area of Revolution and Arc Length

LinkBack

Thread Tools

Display

Finding the Surface Area of Revolution and Arc Length

Similar Math Help Forum Discussions

Surface Area of a Revolution

Area of a Surface of Revolution

Arc Length and Area Surface by revolution

Finding R(x) with area of a surface of revolution

area of surface of revolution

Search Tags