1. ## Surface Area

What is the area of the surface generated wheny=((x^3)/6)+((1)/2x), from x=1, to x=3?

2. You really need to give more information than that. What object are we finding the surface area of?

3. ok i rewrote the question.

4. Ok I think you are after the following equation

$\displaystyle SA = 2\pi \int_1^3 f(x) \sqrt{1+[f'(x)]^2} dx$

where $\displaystyle f(x) =\frac{x^3}{6}+\frac{1}{2x}$

can you find $\displaystyle f'(x)$ ?

5. derivative=((x^2)/2)+((1)/-2x^2)

6. using that equation i get 214pie/9. Is that right?

7. Originally Posted by chevy900ss
derivative=((x^2)/2)+((1)/-2x^2)
Not quite but a good effort.

$\displaystyle f'(x) = \frac{x^2}{2}-\frac{2}{x^2}$

8. how is it -((2)/(x^2). I thought ((1)/2x) is the same as ((x^-1)/2) where you bring the (-1) down front and subtract (1) from the exponent which gives you -((x^-2)/2). Which is -1/2x^2

9. After a second look you are correct

$\displaystyle f'(x) = \frac{x^2}{2}-\frac{1}{2x^2}$