Question

Find the length of the following curve:

y=(1/27)(9x^2+6)^3/2 from x=3 to x=6

Answer 1

arc length?

Answer 2

Yes!

Answer 3

\[L =\int\limits_{a}^{b} ds\]

Answer 4

So what part is troubling you?

Answer 5

\[L = \int\limits_{a}^{b} \sqrt{1+[f'(x)]^2} dx\]

Answer 6

The integration process of the question

Answer 7

Did you set it up

Answer 8

\[\huge f(x) = \frac{ 1 }{ 27 }(9x^2+6)^{\frac{ 3 }{ 2 }}\]

Answer 9

First step, lets find the derivative. Can you do that now please.

Answer 10

\[L = \int\limits_{3}^{6} \sqrt{1+(x \sqrt{9x^2+6})^{2}} dy\]

Answer 11

Is this correct so far?

Answer 12

Yes, that's right. It's better to put it on in later. So with that said, can you square that now, and tell me what you get?

Answer 13

\[L = \int\limits_{3}^{6} \sqrt{1+(x^2(9x^2 + 6))} \]

Answer 14

Yes, make sure to add the dx

Answer 15

Simplify and integrate now.

Answer 16

ok! Do I simplify the radical now?

Answer 17

Gotcha

Answer 18

Inside the radical if you simplify it you'll get \[(3x^2+1)^2\]

Answer 19

Should be simple from there :P

Answer 20

Came back to check up on ya, doing good?

Answer 21

How'd you get (3x^2+1)^2 from that? Just trying to check my simplification