(my first dealings with latex.. so bare with me if this looks a little messed up at first )(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Find the surface area for the equation:

[tex]x = 3y^{4/3} - \frac{3}{32}y^{2/3}[/tex]

with bounds [tex]-216 \leq y \leq 216[/tex]

rotated about the Y-axis.

2. Relevant equations

[tex]\int^a_b 2\pi f(y) \sqrt{1+(\frac{dx}{dy})^2}[/tex]

3. The attempt at a solution

well... going with that equation i get to this point:

[tex]2\pi \int^{216}_{-216} (3y^{4/3} - \frac{3}{32}y^{2/3})(4y^{1/3} + \frac{1}{16}y^{-1/3}) [/tex]

from there I tried to multiply out the equation and solve the integral with the bounds, but it isn't giving me the correct answer. I'm not sure what I'm doing wrong. I suspect I have to break the integral up smaller pieces but im not sure where to break it at.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Surface area of a revolution

**Physics Forums | Science Articles, Homework Help, Discussion**