Question

Find the length of the curve y= (9-3x)^1/2...

Answer 1

I dont think we can find the length of that. That's an infinite curve. Specify the part of the curve whose length is to be found

Answer 2

X=0,x=3 I suppose...

Answer 3

\[=\int\limits_{0}^{3}\sqrt{1+f'(x)^{2}} dx\]

Answer 4

\[f'(x) = \frac{-3}{2\sqrt{9-3x}}\]

Answer 5

\[\rightarrow \int\limits_{0}^{3}\sqrt{\frac{15-4x}{12-4x}} dx\]

Answer 6

I ended up getting 27.86

Answer 7

How did You derive that last one?

Answer 8

here is the solution from wolfram

http://www.wolframalpha.com/input/?i=integrate+sqrt%28%2815-4x%29%2F%2812-4x%29%29+dx+from+0+to+3

Answer 9

oh when you square f'(x) you get:
9/(36-12x) = 3/(12-4x)
add the 1, combine fractions
--> 15-4x/ 12-4x

Answer 10

Just tried it... Doesnt look like the curve I have pictured here. The curve looks like this : http://www.wolframalpha.com/input/?i=integrate+%28%289-3x%29%5E1%2F2%2Cx%2C0%2C3%29

Answer 11

yes, but thats for area under the curve
you want length of the curve right?

Answer 12

yes...I dont understand which formula to use

Answer 13

http://en.wikipedia.org/wiki/Arc_length

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

Answer 14

And what numbers do I apply? How?